Brain-inspired, neuromorphic computing aims to address the growing computational complexity and power consumption in modern von-Neumann architectures. Progress in this area has been hindered due to the lack of hardware elements that can mimic neuronal/synaptic behavior which form the fundamental building blocks for spiking neural networks (SNNs). In this work, we leverage the short/long term memory effects due to the electron trapping events in an atomically thin channel transistor that mimic the exchange of neurotransmitters and emulate a synaptic response. Re-doped (n-type) and Nb-doped (p-type) molybdenum di-sulfide (MoS2) field-effect transistors are examined using pulsed-gate measurements, which identify the time scales of electron trapping/de-trapping. The devices demonstrate promising trends for short/long term plasticity in the order of ms/minutes, respectively. Interestingly, pulse paired facilitation (PPF), which quantifies the short-term plasticity, reveal time constants (τ1 = 27.4 ms, τ2 = 725 ms) that closely match those from a biological synapse. Potentiation and depression measurements describe the ability of the synaptic device to traverse several analog states, where at least 50 conductance values are accessed using consecutive pulses of equal height and width. Finally, we demonstrate devices, which can emulate a well-known learning rule, spike time-dependent plasticity (STDP) which codifies the temporal sequence of pre- and post-synaptic neuronal firing into corresponding synaptic weights. These synaptic devices present significant advantages over iontronic counterparts and are envisioned to create new directions in the development of hardware for neuromorphic computing. © 2020, The Author(s).