Spatio-temporal processes are ubiquitous in nature, science, and engineering. With recent advances in sensor technology and the widespread adoption of, for example, mobile and 5G internet of things devices, cost-efficient large-scale data collection and processing of such processes has become feasible. However, exploiting these opportunities faces several challenges, including privacy issues and limitations in the energy budget, computational power, and connectivity of the participating devices. This project addresses these challenges by developing a new framework for machine learning in spatio-temporal systems that takes these limitations into account. This is realized by leveraging federated learning together with state-of-the-art sequential Bayesian inference methods. In particular, we first develop the fundamental theory governing the problem, followed by developing practical methods based on Kalman filtering, sequential Markov chain Monte Carlo, and non-parametric Bayesian modeling for different classes of spatio-temporal models with increasing complexity. This enables methodologically sound, fully Bayesian inference in numerous applications, taking the devices’ inherent limitations into account and ensuring that their full potential can be leveraged.