The aim of this chapter is to show how the comparison systems are used for studying the stability of dynamical systems. The already known methods based on the use of positive definite vector Lyapunov-like functions are extended to the case where signed-indefinite vector Lyapunov-like functions are used for the stability analysis. In this general framework, methods of studying quadratic and polyhedral robust stability are presented. Particular attention is paid to the stability analysis of nonlinear comparison systems using converse comparison systems.