This authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric Bayesian, and deep learning methods. Details are provided on practical applications in neural and clinical data, whether this is characterising time series data from neural spike trains recorded from the rat hippocampus, the primate motor cortex, or the human EEG, MEG or fMRI, or physiological measurements of heartbeats or blood pressures. With real-world case studies of neuroscience experiments and clinical data sets, and written by expert authors from across the field, this is an ideal resource for anyone working in neuroscience and physiological data analysis.