The miniaturization of ferroelectric devices offers prospects for non-volatile memories, low-power electrical switches and emerging technologies beyond existing Si-based integrated circuits. An emerging class of ferroelectrics is based on van der Waals (vdW) two-dimensional materials with potential for nano-ferroelectrics. Here, we report on ferroelectric semiconductor junctions (FSJs) in which the ferroelectric vdW semiconductor α-In2Se3 is embedded between two single-layer graphene electrodes. In these two-terminal devices, the ferroelectric polarization of the nanometre-thick In2Se3 layer modulates the transmission of electrons across the graphene/In2Se3 interface, leading to memristive effects that are controlled by applied voltages and/or by light. The underlying mechanisms of conduction are examined over a range of temperatures and under light excitation revealing thermionic injection, tunnelling and trap-assisted transport. These findings are relevant to future developments of FSJs whose geometry is well suited to miniaturization and low-power electronics, offering opportunities to expand functionalities of ferroelectrics by design of the vdW heterostructure.