The recent progress of selector and self-rectifying devices for resistive randomaccess memory applications is reviewed. In particular, the performance of crossbar arrays based on resistive switching (RS) devices, the sneak-path current issue, and possible solutions is discussed. The parameters and requirements of selector devices are elucidated here, and several types of selector devices, such as a transistor-assisted transistor-one resistor, unipolar one diode-one resistor, bipolar one selector-one resistor, and threshold switching selectors, are comprehensively discussed. In the case of self-rectifying devices, the recent progress in complementary RS devices, vacancy-modulated conductive oxide-based devices, and tunneling barrier-based RS devices is reviewed. The switching mechanisms and the geometrical configuration of the selector and self-rectifying RS devices are emphasized. Furthermore, comparative assessments of the different devices are evaluated. Finally, an overview of the gaps in previously reported devices is presented and some key improvements for future research direction suggested.