We focus on dynamical descriptions of short-term synaptic plasticity. Instead of focusing on the molecular machinery that has been reviewed recently by several authors, we concentrate on the dynamics and functional significance of synaptic plasticity, and review some mathematical models that reproduce different properties of the dynamics of short term synaptic plasticity that have been observed experimentally. The complexity and shortcomings of these models point to the need of simple, yet physiologically meaningful models. We propose a simplified model to be tested in synapses displaying different types of short-term plasticity.