When deposited on a superheated surface, a droplet can be levitated by its own vapour layer, a phenomenon that is referred to as the Leidenfrost effect. This dynamic effect has attracted interest for many potential applications, such as cooling, drag reduction and drop transport. A lot of effort has been paid to this mechanism over the past two and half centuries. Herein, we not only review the classical theories but also present the most recent theoretical advances in understanding the Leidenfrost effect. We first review the basic theories of the Leidenfrost effect, which mainly focuses on the relationship between the drop shape, vapour layer and lifetime. Then, the shift in the Leidenfrost point realized by fabricating special surface textures is introduced and the mechanisms behind this are analyzed. Furthermore, we present the reasons for the droplet transport in both classical Leidenfrost and pseudo-Leidenfrost regimes. Finally, the promising breakthroughs of the Leidenfrost effect are briefly addressed.