A finite state machine (FSM, or automaton) is an abstract machine that can switch among a finite number of states in response to temporally ordered inputs, which allows storage and processing of information in an order-sensitive manner. In recent decades, DNA molecules have been actively exploited to develop information storage and nanoengineering materials, which hold great promise for smart nanodevices and nanorobotics under the framework of FSM. In this review, we summarize recent progress in utilizing DNA self-assembly and DNA nanostructures to implement FSMs. We describe basic principles for representative DNA FSM prototypes and highlight their advantages and potential in diverse applications. The challenges in this field and future directions have also been discussed.