Wide bandgap (WBG) devices offer the advantages of high frequency, high efficiency, and high power density to power converters due to their excellent performance. However, their low parasitic capacitance and fast switching speed also make them more susceptible to switching oscillations. The switching oscillations can cause voltage and current overshoots, shoot-through, electromagnetic interference, additional power loss, and even device damage, which can seriously affect the performance of power converters and systems. However, a comprehensive and in-depth overview is lacking on this topic. This article reviews the types, the causes and negative effects, the effects of parasitic parameters and suppression methods of these switching oscillations, which is helpful for practical engineering. First, the switching oscillations are divided into different types, and their causes and negative effects are reviewed. Then, the effects of different parasitic parameters on the switching oscillations are overviewed. It is found that due to the different physical structures of silicon carbide metal-oxide-semiconductor field-effect transistors, enhancement-mode gallium nitride high-electron mobility transistors (eGaN HEMTs), and cascode GaN HEMTs, the effects are also different. Finally, the main methods of suppressing the switching oscillations are summarized, and the advantages and disadvantages of these methods are presented. Furthermore, future research works on this topic and the conclusion of this paper are drawn, which will help readers deepen their understanding of the switching oscillations of WBG devices, and inspire readers to better use WBG devices for high-frequency and high-efficient power conversion.