This chapter deals with the presentation of the basic theory related to digital filters. After the presentation of the basic concepts and the comparison of digital and analog filters, the basic types of digital filters are presented, such as finite and infinite impulse response filters (FIRs and IIRs), ideal and real digital filters, as well as filters with generalized linear phase. Then, the design procedure of digital filters is presented in detail and many related aspects and procedures, such as the determination of the filter requirements, the estimation of the filter coefficients, and the construction of the filter transfer function, are discussed. Then, we focus on the presentation of the basic theory associated with the representation of integers and floating point numbers in digital systems (such as the sign-magnitude representation as well as the ones’ and the two’s complement), together with the implementation of addition and multiplication, we well as the structure and the operation of the serial parallel adders and multipliers used in digital systems. The impact of overflow, as well as the associated quantization and overflow errors, is examined in detail. Additionally, we discuss how the limited word length of system registers influences the accuracy of operations involving the multiplication of real and complex numbers. The undesirable phenomenon of limit cycles is analyzed in detail, together with techniques that allow the elimination of such cycles. The concept of causality in the domain of digital filters is analyzed and the FIR filters are presented in detail. The rest of the chapter deals with well-known digital filter design techniques and tools such as the window method, the frequency sampling method, and the Remez and Parks-McClellan algorithms for FIR filters, together with the impulse invariance, the bilinear transformation, as well as least-squares and optimization methods for IIR filters. The representation of digital filters with signal flow graphs is also presented. The chapter concludes with the presentation of the basic implementations of digital filters (serial and parallel form and frequency sampling form) and the concept of digital filter transformations is also discussed.