Memristive devices have been extensively demonstrated for applications in nonvolatile memory, computer logic, and biological synapses. Precise control of the conducting paths associated with the resistance switching in memristive devices is critical for optimizing their performances including ON/OFF ratios. Here, gate tunability and multidirectional switching can be implemented in memristors for modulating the conducting paths using hexagonal α-In2Se3, a semiconducting van der Waals ferroelectric material. The planar memristor based on in-plane (IP) polarization of α-In2Se3 exhibits a pronounced switchable photocurrent, as well as gate tunability of the channel conductance, ferroelectric polarization, and resistance-switching ratio. The integration of vertical α-In2Se3 memristors based on out-of-plane (OOP) polarization is demonstrated with a device density of 7.1 × 109 in.−2 and a resistance-switching ratio of well over 103. A multidirectionally operated α-In2Se3 memristor is also proposed, enabling the control of the OOP (or IP) resistance state directly by an IP (or OOP) programming pulse, which has not been achieved in other reported memristors. The remarkable behavior and diverse functionalities of these ferroelectric α-In2Se3 memristors suggest opportunities for future logic circuits and complex neuromorphic computing.