Computational neuroscience is an appealing interdisciplinary domain, at the interface between biology and computer science. It aims at understanding the experimental data obtained in neuroscience using several different kinds of models, one of which being artificial neural networks. In this tutorial we review some of the advances neural networks have achieved in computational neuroscience, and in particular focusing on spiking neural networks. Several artificial neuron models, that are able to account for the temporal properties of biological neurons, are described. We also describe briefly data obtained using conventional neuroscience methods, and some artificial neural networks developed to understand the mechanisms underlying these experimental data.