This thesis addresses the development of Bayesian methods for the joint analysis of spatial panel data with nonstandard features. Nonstandardness comes in many forms, including nonstationarity, mixed discrete-continuous observations, and heavy tails. Mixture models provide a flexible statistical framework for handling these features, and in this thesis we develop hierarchical mixtures for nonstandard spatial panel data. We develop Markov chain Monte Carlo algorithms for these models capable of scaling to settings of high dimensionality, both in the data and the model parameters. Applications are described to simulated data, disease incidence counts, and the climate analysis of Australian rainfall data.