This chapter explains the fundamental theory of incoherent and coherent optical signal processing, which provides the basis for later chapters. The advantages and disadvantages of incoherent and coherent optical systems and means of overcoming their limitations are outlined in Section 2.1. The characteristics of the fundamental components of incoherent fiber-optic signal processors (Section 2.2) and coherent integrated-optic signal processors (Section 2.3) are then described.