This chapter focuses on the main aspects of adaptive signal processing. The basic concepts are introduced in a simple framework, and its main applications (namely system identification, channel equalization, signal prediction, and noise cancellation) are briefly presented. Several adaptive algorithms are presented, and their convergence behaviors are analyzed. The algorithms considered in this chapter include the popular least-mean square (LMS), its normalized-LMS version, the affine-projection with the set-membership variation, the recursive least-squares (RLS), the transform-domain, the sub-band domain, and some IIR-filter algorithms such as the equation-error (EE) and the output-error (OE) algorithms. The main purpose of all this presentation is to give general guidelines for the reader to choose the most adequate technique for the audio application at hand.