Memristors are two-terminal passive circuit elements that have been developed for use in non-volatile resistive random-access memory and may also be useful in neuromorphic computing(1-6). Memristors have higher endurance and faster read/write times than flash memory(4,7,8) and can provide multi-bit data storage. However, although two-terminal memristors have demonstrated capacity for basic neural functions, synapses in the human brain outnumber neurons by more than a thousandfold, which implies that multi-terminal memristors are needed to perform complex functions such as heterosynaptic plasticity(3,9-13). Previous attempts to move beyond two-terminal memristors, such as the three-terminal Widrow-Hoff memristor(14) and field-effect transistors with nanoionic gates(15) or floating gates(16), did not achieve memristive switching in the transistor(17). Here we report the experimental realization of a multi-terminal hybrid memristor and transistor (that is, a memtransistor) using polycrystalline monolayer molybdenum disulfide (MoS2) in a scalable fabrication process. The two-dimensional MoS2 memtransistors show gate tunability in individual resistance states by four orders of magnitude, as well as large switching ratios, high cycling endurance and long-term retention of states. In addition to conventional neural learning behaviour of long-term potentiation/ depression, six-terminal MoS2 memtransistors have gate-tunable heterosynaptic functionality, which is not achievable using two-terminal memristors. For example, the conductance between a pair of floating electrodes (pre-and post-synaptic neurons) is varied by a factor of about ten by applying voltage pulses to modulatory terminals. In situ scanning probe microscopy, cryogenic charge transport measurements and device modelling reveal that the bias-induced motion of MoS2 defects drives resistive switching by dynamically varying Schottky barrier heights. Overall, the seamless integration of a memristor and transistor into one multi-terminal device could enable complex neuromorphic learning and the study of the physics of defect kinetics in two-dimensional materials(18-22).