This chapter presents a comprehensive description of the use of piecewise-linear (PWL) methods in modeling, analysis, and structural properties of nonlinear circuits. It provides complete hierarchy of models and representations of models. The chapter examines the piecewise-linear models for several important electronic components. It discusses the structural properties of piecewise-linear circuits since many PWL properties are preserved by interconnection. The chapter explores analysis methods of PWL circuits, ranging from the J. Katzenelson algorithm to the linear complementarity methods and the homotopy methods. It describes efficient computer-aided analysis of PWL circuits and the hierarchical mixed-mode PWL analysis. In order to situate these subjects in the general framework of nonlinear circuits, it is instructive to interrelate the PWL circuit analysis methods. The chapter shows the conversion from a circuit to a set of equations by network equation formulation and the conversion from equations to solutions by solution methods.