The proposed research focuses on stochastic models for evaluating and optimising the performance of large-scale wireless networks. Future wireless networks will not just support human-to-human communications, but also serve as a platform for content dissemination and provide the main artery of the `Internet of things', connecting massive numbers of electronic devices and sensors. In the absence of centralised infrastructure, these emerging networks vitally depend on the individual nodes to operate autonomously and efficiently share the medium in a distributed fashion. Randomised algorithms provide a popular mechanism for distributed medium-access control in such environments, and exciting recent findings suggest that these mechanisms have the capability to achieve near-optimal performance. A further key source of randomness in wireless networks arises from user mobility, which provides scope for improving the performance through opportunistic scheduling. Achieving the full potential of random medium-access algorithms and leveraging user mobility for improving the performance are extremely challenging goals, which raise an urgent need for novel stochastic models.