Composite material consumption is booming and is expected to increase exponentially in many industrial applications such as aerospace, automotive, marine and defense. However, in most cases, composite products require further processing before they can be used or assembled. Machining of composite materials is extremely difficult due to their anisotropic and non-homogeneous structure. This paper provides a comprehensive review of the literature on composite materials and their machining processes, such as turning, milling and drilling. Damage related to these processes is also discussed. The paper is divided into seven main parts; the first, second and third parts give a brief overview of composite materials, reinforcements used in composite materials and composite manufacturing methods, respectively. The fourth part deals with post-processing machining operations, while the fifth, sixth and seventh parts are devoted to the machining of carbon fiber reinforced polymer composite, glass fiber reinforced polymer and natural fiber reinforced polymer composites, respectively. An analysis of the factors that influence the machining and the machinability criteria used for these materials is also presented, with particular emphasis on cutting forces, tool wear, delamination and surface finish. Non-traditional manufacturing methods are not discussed in this paper.