Integrable deformations of type IIB superstring theory on $\mathrm{AdS}_5\times S^5$ have played an important role over the last years. The Yang-Baxter deformation is a systematic way of generating such integrable deformations. Since its introduction, this topic has seen important conceptual progress and has among others led to the intriguing discovery generalized supergravity, a new low-energy effective theory. This review endeavors to not only introduce the historical development of the Yang-Baxter deformation, but also its relation to generalized supergravity, non-geometric backgrounds, non-abelian T-duality and preserved Killing spinors. We supplement the general treatment with a wealth of explicit examples.