In this chapter, an overview is provided of the types of fibre and matrix in common use and of how they are assembled into composites. Many types of reinforcement, mostly fibres, are available commercially. Their properties are related to atomic structure and the presence of defects, which must be controlled during manufacture. Matrices may be based on polymers, metals or ceramics. Choice of matrix is usually related to required properties, component geometry and method of manufacture. Certain composite properties may be sensitive to the nature of the reinforcement/matrix interface; this topic is covered in Chapter 7. Properties are also dependent on the arrangement and distribution of fibres, i.e. the fibre architecture, an expression that encompasses intrinsic features of the fibres, such as their diameter and length, as well as their volume fraction, alignment and spatial distribution. Fibre arrangements include laminae (sheets containing aligned long fibres) and laminates that are built up from these. Other continuous fibre systems, such as woven configurations, are also covered. Short fibre systems can be more complex and methods of characterising them are also briefly described.