Spatial device-to-device communications are expected to play a key role in future communication systems. Their often high complexity can, at least in part, be modelled with the help of a probabilistic approach, where the network components are considered to be a stochastic point process. In this talk, I will introduce some of the most important ingredients in the theory of stochastic geometry, and present examples on how we use them to study for example malware propagation in device-to-device networks or bottleneck behavior for the connectivity in such networks.