This review article aims at summarizing the basic principles of circuit methods used in compact pulsed-power generators. The concept of energy storage and voltage adding are explained followed by the descriptions on switching unit design and control signal generation. Some examples of applications of these circuit methods are given, including Marx circuit using capacitor energy storage, Marx circuit using inductive energy storage, Marx circuit using hybrid energy storage, linear transformer driver (LTD) circuit using capacitive energy storage and LTD circuit using inductive energy storage.