diff --git a/Changes b/Changes
index dee3877b30..8df251f0d6 100644
--- a/Changes
+++ b/Changes
@@ -14,6 +14,8 @@ Breaking Changes
 ----------------
 
 - Canceller : Changed base class.
+- MessageHandler : Removed support for passing `boost::format` objects to `msg()`. Use `fmt::format()` instead.
+- FileSequence : Removed `fileNameTemplate()` protected method. Use `fileNameForFrame()` instead.
 
 Build
 -----
diff --git a/include/IECore/FileSequence.h b/include/IECore/FileSequence.h
index 1df824527c..6d38643124 100644
--- a/include/IECore/FileSequence.h
+++ b/include/IECore/FileSequence.h
@@ -39,7 +39,6 @@
 #include "IECore/FrameList.h"
 #include "IECore/RunTimeTyped.h"
 
-#include "boost/format.hpp"
 #include "boost/regex.hpp"
 
 #include <string>
@@ -132,11 +131,6 @@ class IECORE_API FileSequence : public RunTimeTyped
 		std::string m_fileName;
 		FrameListPtr m_frameList;
 
-		/// Returns a boost::format for expanding out the filename with a frame number. Due to limitations in boost::format
-		/// we need use a different template depending on the sign of the frame number.
-		boost::format fileNameTemplate( bool negativeFrame ) const;
-
-
 };
 
 } // namespace IECore
diff --git a/include/IECore/MessageHandler.h b/include/IECore/MessageHandler.h
index ec4889066e..8030a3bdf8 100644
--- a/include/IECore/MessageHandler.h
+++ b/include/IECore/MessageHandler.h
@@ -38,7 +38,6 @@
 #include "IECore/Export.h"
 #include "IECore/RefCounted.h"
 
-#include "boost/format.hpp"
 #include "boost/noncopyable.hpp"
 
 #include "fmt/format.h"
@@ -82,8 +81,6 @@ class IECORE_API MessageHandler : public RefCounted
 		//@{
 		/// Output a message to the current handler.
 		static void output( Level level, const std::string &context, const std::string &message );
-		/// Output a message to the current handler.
-		static void output( Level level, const std::string &context, const boost::format &message );
 		//@}
 
 		//! @name Default handler
@@ -156,7 +153,6 @@ typedef MessageHandler Msg;
 /// Free functions which calls MessageHandler::output() with their arguments. These are provided
 /// for brevity.
 IECORE_API void msg( MessageHandler::Level level, const std::string &context, const std::string &message );
-IECORE_API void msg( MessageHandler::Level level, const std::string &context, const boost::format &message );
 /// Inline templated convenience function which formats the message using the provided arguments.
 template <typename... Args>
 inline void msg( MessageHandler::Level level, const std::string &context, fmt::format_string<Args...> message, Args&&... args )
diff --git a/src/IECore/FileSequence.cpp b/src/IECore/FileSequence.cpp
index c04a5ecfc2..7a359e8a8c 100644
--- a/src/IECore/FileSequence.cpp
+++ b/src/IECore/FileSequence.cpp
@@ -37,7 +37,6 @@
 #include "IECore/Exception.h"
 
 #include "boost/algorithm/string.hpp"
-#include "boost/format.hpp"
 #include "boost/lexical_cast.hpp"
 #include "boost/regex.hpp"
 
@@ -198,7 +197,9 @@ void FileSequence::setSuffix( const std::string &suffix )
 
 std::string FileSequence::fileNameForFrame( FrameList::Frame frameNumber ) const
 {
-	return ( fileNameTemplate( frameNumber < 0 ) % frameNumber ).str();
+	return fmt::format(
+		"{0}{1:0{2}}{3}", getPrefix(), frameNumber, getPadding() + ( frameNumber < 0 ? 1 : 0 ), getSuffix()
+	);
 }
 
 FrameList::Frame FileSequence::frameForFileName( const std::string &fileName ) const
@@ -225,17 +226,12 @@ void FileSequence::fileNames( std::vector< std::string > &f ) const
 {
 	f.clear();
 
-	boost::format posFmt = fileNameTemplate( false );
-	boost::format negFmt = fileNameTemplate( true );
-
 	std::vector< FrameList::Frame > frames;
-
 	m_frameList->asList( frames );
 
-	for ( std::vector< FrameList::Frame >::const_iterator it = frames.begin(); it != frames.end(); ++it )
+	for( auto frame : frames )
 	{
-		boost::format &fmt = *it < 0 ? negFmt : posFmt ;
-		f.push_back( ( fmt % *it ).str() );
+		f.push_back( fileNameForFrame( frame ) );
 	}
 }
 
@@ -243,23 +239,16 @@ void FileSequence::clumpedFileNames( unsigned clumpSize, std::vector< std::vecto
 {
 	f.clear();
 
-	boost::format posFmt = fileNameTemplate( false );
-	boost::format negFmt = fileNameTemplate( true );
-
 	std::vector< std::vector< FrameList::Frame > > clumpedFrames;
 
 	m_frameList->asClumpedList( clumpedFrames, clumpSize );
 
-	for ( std::vector< std::vector< FrameList::Frame > >::const_iterator it = clumpedFrames.begin(); it != clumpedFrames.end(); ++it )
+	for( const auto &clump : clumpedFrames )
 	{
-		const std::vector< FrameList::Frame > &clump = *it;
-
 		f.push_back( std::vector< std::string >() );
-
-		for ( std::vector< FrameList::Frame > ::const_iterator cit = clump.begin(); cit != clump.end(); ++cit )
+		for( auto frame : clump )
 		{
-			boost::format &fmt = *cit < 0 ? negFmt : posFmt ;
-			f.back().push_back( ( fmt % *cit ).str() );
+			f.back().push_back( fileNameForFrame( frame ) );
 		}
 	}
 }
@@ -325,19 +314,3 @@ bool FileSequence::operator ==( const FileSequence &other ) const
 {
 	return m_fileName == other.m_fileName && m_frameList->isEqualTo( other.m_frameList );
 }
-
-boost::format FileSequence::fileNameTemplate( bool negativeFrame ) const
-{
-	unsigned padding = getPadding();
-	std::string paddingStr = "";
-	for ( unsigned i = 0; i < padding; i++)
-	{
-		paddingStr += "#";
-	}
-
-	std::string f = m_fileName;
-	boost::replace_all( f, "%", "%%" );
-	boost::replace_all( f, paddingStr, ( boost::format( "%%0%dd" ) % ( negativeFrame ? padding + 1 : padding ) ).str() );
-
-	return boost::format( f );
-}
diff --git a/src/IECore/MessageHandler.cpp b/src/IECore/MessageHandler.cpp
index 73f4e673e3..834fd04491 100644
--- a/src/IECore/MessageHandler.cpp
+++ b/src/IECore/MessageHandler.cpp
@@ -56,12 +56,6 @@ void MessageHandler::output( Level level, const std::string &context, const std:
 	currentHandler()->handle( level, context, message );
 }
 
-void MessageHandler::output( Level level, const std::string &context, const boost::format &message )
-{
-	string m = message.str();
-	output( level, context, m );
-}
-
 ///////////////////////////////////////////////////////////////////////////////////////
 // default handler
 ///////////////////////////////////////////////////////////////////////////////////////
@@ -173,8 +167,3 @@ void IECore::msg( MessageHandler::Level level, const std::string &context, const
 {
 	MessageHandler::output( level, context, message );
 }
-
-void IECore::msg( MessageHandler::Level level, const std::string &context, const boost::format &message )
-{
-	MessageHandler::output( level, context, message );
-}
diff --git a/src/IECoreGL/Selector.cpp b/src/IECoreGL/Selector.cpp
index 5a2ce33f2c..ecf8317ae9 100644
--- a/src/IECoreGL/Selector.cpp
+++ b/src/IECoreGL/Selector.cpp
@@ -306,7 +306,7 @@ class Selector::Implementation : public IECore::RefCounted
 		//////////////////////////////////////////////////////////////////////////
 
 		FrameBufferPtr m_frameBuffer;
-		boost::shared_ptr<FrameBuffer::ScopedBinding> m_frameBufferBinding;
+		std::unique_ptr<FrameBuffer::ScopedBinding> m_frameBufferBinding;
 		GLint m_prevProgram;
 		ConstShaderPtr m_currentIDShader;
 		std::stack<ConstShaderPtr> m_IDShaderStack;
@@ -325,7 +325,7 @@ class Selector::Implementation : public IECore::RefCounted
 			}
 			m_frameBuffer->setDepth( new DepthTexture( 128, 128 ) );
 			m_frameBuffer->validate();
-			m_frameBufferBinding = boost::shared_ptr<FrameBuffer::ScopedBinding>( new FrameBuffer::ScopedBinding( *m_frameBuffer ) );
+			m_frameBufferBinding = std::make_unique<FrameBuffer::ScopedBinding>( *m_frameBuffer );
 
 			glGetIntegerv( GL_VIEWPORT, m_prevViewport );
 			glViewport( 0, 0, 128, 128 );
diff --git a/src/IECoreImage/ImagePrimitive.cpp b/src/IECoreImage/ImagePrimitive.cpp
index 3257766067..7ce334a006 100644
--- a/src/IECoreImage/ImagePrimitive.cpp
+++ b/src/IECoreImage/ImagePrimitive.cpp
@@ -41,6 +41,8 @@
 
 #include "boost/static_assert.hpp"
 
+#include "fmt/format.h"
+
 #include <cassert>
 
 using namespace std;
@@ -406,7 +408,7 @@ bool ImagePrimitive::channelValid( const IECore::Data *data, std::string *reason
 	{
 		if( reason )
 		{
-			*reason = str( format( "Channel has wrong size (%d but should be %d)." ) % size % numPixels );
+			*reason = fmt::format( "Channel has wrong size ({} but should be {}).", size, numPixels );
 		}
 		return false;
 	}
@@ -421,7 +423,7 @@ bool ImagePrimitive::channelValid( const std::string &name, std::string *reason
 	{
 		if( reason )
 		{
-			*reason = str( format( "Channel \"%s\" does not exist." ) % name );
+			*reason = fmt::format( "Channel \"{}\" does not exist.", name );
 		}
 		return false;
 	}
diff --git a/src/IECoreScene/Font.cpp b/src/IECoreScene/Font.cpp
index ce2241fc4a..df124742fe 100644
--- a/src/IECoreScene/Font.cpp
+++ b/src/IECoreScene/Font.cpp
@@ -476,9 +476,7 @@ class Font::Implementation : public IECore::RefCounted
 			V2f advance;
 		};
 
-		typedef boost::shared_ptr<Mesh> MeshPtr;
-		typedef boost::shared_ptr<const Mesh> ConstMeshPtr;
-		mutable std::vector<MeshPtr> m_meshes;
+		mutable std::vector<std::unique_ptr<Mesh>> m_meshes;
 
 		const Mesh *cachedMesh( char c ) const
 		{
@@ -511,11 +509,11 @@ class Font::Implementation : public IECore::RefCounted
 			transformOp->operate();
 
 			// put it in the cache
-			MeshPtr mesh( new Mesh );
+			auto &mesh = m_meshes[c];
+			mesh = std::make_unique<Mesh>();
 			mesh->primitive = primitive;
 			mesh->bound = primitive->bound();
 			mesh->advance = V2f( m_face->glyph->advance.x, m_face->glyph->advance.y ) / m_face->units_per_EM;
-			m_meshes[c] = mesh;
 
 			// return it
 			return mesh.get();
diff --git a/src/IECoreScene/PDCParticleReader.cpp b/src/IECoreScene/PDCParticleReader.cpp
index 0057c5ef81..6942e77ce5 100644
--- a/src/IECoreScene/PDCParticleReader.cpp
+++ b/src/IECoreScene/PDCParticleReader.cpp
@@ -124,7 +124,7 @@ bool PDCParticleReader::open()
 
 		if( m_header.version > 1 )
 		{
-			msg( Msg::Warning, "PDCParticleReader::open()", format( "File \"%s\" has unknown version %d." ) % fileName() % m_header.version );
+			msg( Msg::Warning, "PDCParticleReader::open()", "File \"{}\" has unknown version {}.", fileName(), m_header.version );
 		}
 
 		int unused = 0;
@@ -262,7 +262,7 @@ DataPtr PDCParticleReader::readAttribute( const std::string &name )
 	const Data *idAttr = idAttribute();
 	if ( !idAttr && particlePercentage() < 100.0f )
 	{
-		msg( Msg::Warning, "PDCParticleReader::filterAttr", format( "Percentage filtering requested but file \"%s\" contains no particle Id attribute." ) % fileName() );
+		msg( Msg::Warning, "PDCParticleReader::filterAttr", "Percentage filtering requested but file \"{}\" contains no particle Id attribute.", fileName() );
 	}
 
 	DataPtr result = nullptr;
diff --git a/src/IECoreScene/PDCParticleWriter.cpp b/src/IECoreScene/PDCParticleWriter.cpp
index 073d9ecf5b..cf85853db3 100644
--- a/src/IECoreScene/PDCParticleWriter.cpp
+++ b/src/IECoreScene/PDCParticleWriter.cpp
@@ -152,7 +152,7 @@ void PDCParticleWriter::doWrite( const CompoundObject *operands )
 		}
 		else
 		{
-			msg( Msg::Warning, "PDCParticleWriter::write", format( "Attribute \"%s\" is of unsupported type \"%s\"." ) % *it % attr->typeName() );
+			msg( Msg::Warning, "PDCParticleWriter::write", "Attribute \"{}\" is of unsupported type \"{}\".", *it, attr->typeName() );
 		}
 	}
 
diff --git a/src/IECoreScene/ParticleReader.cpp b/src/IECoreScene/ParticleReader.cpp
index 4f78a76b21..ac061b0ac6 100644
--- a/src/IECoreScene/ParticleReader.cpp
+++ b/src/IECoreScene/ParticleReader.cpp
@@ -190,7 +190,7 @@ ObjectPtr ParticleReader::doOperation( const CompoundObject * operands )
 			}
 			else
 			{
-				msg( Msg::Warning, "ParticleReader::doOperation", format( "Ignoring attribute \"%s\" due to insufficient elements (expected %d but found %d)." ) % *it % result->getNumPoints() % s );
+				msg( Msg::Warning, "ParticleReader::doOperation", "Ignoring attribute \"{}\" due to insufficient elements (expected {} but found {}).", *it, result->getNumPoints(), s );
 			}
 		}
 		else if ( testTypedData<TypeTraits::IsSimpleTypedData>( d.get() ) )
diff --git a/src/IECoreScene/ParticleWriter.cpp b/src/IECoreScene/ParticleWriter.cpp
index b7bd3ff572..0368514c15 100644
--- a/src/IECoreScene/ParticleWriter.cpp
+++ b/src/IECoreScene/ParticleWriter.cpp
@@ -95,7 +95,7 @@ void ParticleWriter::particleAttributes( std::vector<std::string> &names )
 			}
 			else
 			{
-				msg( Msg::Warning, "ParticleWriter::particleAttributes", format( "Ignoring attribute \"%s\" due to insufficient elements (expected %d but found %d)." ) % it->first % numParticles % s );
+				msg( Msg::Warning, "ParticleWriter::particleAttributes", "Ignoring attribute \"{}\" due to insufficient elements (expected {} but found {}).", it->first, numParticles, s );
 			}
 		}
 		else if ( testTypedData<TypeTraits::IsSimpleTypedData>( it->second.data.get() ) )
@@ -124,7 +124,7 @@ void ParticleWriter::particleAttributes( std::vector<std::string> &names )
 		}
 		else
 		{
-			msg( Msg::Warning, "ParticleWriter::particleAttributes", format( "Attribute \"%s\" requested via parameters but is not available." ) % *it );
+			msg( Msg::Warning, "ParticleWriter::particleAttributes", "Attribute \"{}\" requested via parameters but is not available.", *it );
 		}
 	}
 }
diff --git a/src/IECoreScene/PointsAlgoSegment.cpp b/src/IECoreScene/PointsAlgoSegment.cpp
index 39a9f20ad9..b1151d2ff4 100644
--- a/src/IECoreScene/PointsAlgoSegment.cpp
+++ b/src/IECoreScene/PointsAlgoSegment.cpp
@@ -39,8 +39,6 @@
 #include "IECore/DespatchTypedData.h"
 #include "IECore/TypeTraits.h"
 
-#include "boost/format.hpp"
-
 using namespace IECore;
 using namespace IECoreScene;
 using namespace Imath;
diff --git a/src/IECoreScene/SceneCache.cpp b/src/IECoreScene/SceneCache.cpp
index 84d8493a94..35ec4e9dd7 100644
--- a/src/IECoreScene/SceneCache.cpp
+++ b/src/IECoreScene/SceneCache.cpp
@@ -1403,7 +1403,7 @@ class SceneCache::WriterImplementation : public SceneCache::Implementation
 				{
 					std::string prefix = "SceneCache::writeObject";
 					std::string details = fmt::format(
-						"object written at previous time: %1%,\nSample times must be written sequentially for each object.",
+						"object written at previous time: {},\nSample times must be written sequentially for each object.",
 						*(m_objectSampleTimes.rbegin())
 					);
 					throwException( prefix, time, details );