Conductance changes in memristors can remain for very long times or relax after a short time. Thus, memristors can be used as electronic synapses and neurons in artificial neural networks implemented in hardware. In this work we use a stochastic compact model for the electrical behaviour of memory switching (MS) and threshold switching (TS) for synapse and neuron functions, respectively. In the case of non-volatile memristors we focus on potentiation/depression transients, programming energy, programming time and power requirements for writing conductance weights in artificial network crossbars. As for TS memristors, we consider the modelling of their behaviour in the context of a leaky-integrate-and-fire neuron, demonstrating how the model captures the threshold activation function and the response as a function of the input signal frequency dependence.