In this chapter, essential properties of fibres required for fabricating good performance composites are presented. Fundamental aspects of these properties and principles of their characterization techniques are discussed. Firstly, the geometrical aspects of fibres (for short and endless fibres) are described. The second part deals with the different types of structures in fibres with respect to molecular orientation mostly responsible for anisotropy of fibres. In the third part, the mechanical properties (especially tensile properties) and failure mechanisms for different types of fibres are discussed and correlated to the structure of the fibres. The following part is concerned with the surface of fibres, which is responsible for the interaction of the fibres with the matrix material in composites and has a large influence on the wetting behavior and adhesion to matrix materials. In the last parts, further physical properties (heat capacity, thermal conductivity, thermomechanical properties and electrical conductivity) and the durability of fibres are described.