Low-temperature plasmas (LTPs) driven by 1-100 MHz radio-frequency (MRF) is essential for many industrial applications, and their breakdown characteristics are different from direct current (DC) breakdown. This review seeks to understand the state of the art of electric breakdown in the MRF field and provide references for related basic and applied research. We have given a brief history of the research of MRF-driven breakdown, including the Paschen curves, the corresponding discharge modes and parameter spaces, and the evolution of the parameters during the breakdown process. It is shown that the focus has been transferred from the breakdown voltage and V-I characters to the evolution of plasma parameters during the breakdown, both in experiments and simulations. It is shown that many fundamental and applied problems still need to be investigated, especially with the new global model and incorporating the external circuit model.