Repetitively pulsed gas volume and dielectric surface discharges have gained growing attention because of peculiar and exciting physics phenomena, high efficiency, high reactivity, and potential to obtain conventionally unachievable plasma properties. Nevertheless, incomplete understanding of fundamental mechanisms renders the repetitively pulsed discharge far less predictable and controllable, where the inherent memory effect and the discharge mode transition are universal challenges. In this topical review, the authors will explore the macroscopic characteristics of the gas gap breakdown and the surface flashover, state‐of‐the‐art mechanisms and dominant agents of discharge memory effects, operation regimes and transitions of the discharge mode, and how waveform parameters affect the pulsed discharge properties. Challenges and potential approaches for further understanding the memory effect and the discharge mode transition in the repetitively pulsed discharge are discussed.