The probabilistic nature of synaptic transmission has remained enigmatic. However, recent developments have started to shed light on why the brain may rely on probabilistic synapses. Here, we start out by reviewing experimental evidence on the specificity and plasticity of synaptic response statistics. Next, we overview different computational perspectives on the function of plastic probabilistic synapses for constrained, statistical and deep learning. We highlight that all of these views require some form of optimisation of probabilistic synapses, which has recently gained support from theoretical analysis of long-term synaptic plasticity experiments. Finally, we contrast these different computational views and propose avenues for future research. Overall, we argue that the time is ripe for a better understanding of the computational functions of probabilistic synapses.