Memristive stateful logic enables complete in-memory computing, allowing low-power and low-cost Boolean computing. Its characteristics are consistent with the requirements of edge computing devices, which will occupy a considerable segment in the coming Internet of things (IoT) era. In this review, recent developments in stateful logic technology are intensively explored. The topics include a summary of the evolution of stateful logic gates and their cascading strategies for Boolean computing. Also, array-level data manipulation is discussed, and its role in realizing massive computation inside the memory. Finally, the logic operation error issue is discussed, with feasible solutions.