The human microbiome is highly dynamic on multiple timescales, changing dramatically during development of the gut in childhood, with diet, or due to medical interventions. I will present two novel Bayesian machine learning methods for gaining insight into microbiome dynamics. The first, MDSINE, is a method for efficiently inferring dynamical systems models from microbiome time-series data. I will present recent extensions to MDSINE including interaction modules, or learned clusters of latent variables (reducing the expected number of interaction coefficients from O(n^2) to O((log n)^2)); a fully Bayesian stochastic dynamical systems formulation that propagates measurement and latent state uncertainty throughout the model; and a temporally varying auxiliary variable technique to enable efficient inference by relaxing hard non-negativity constraints on states. The second method, Microbiome Interpretable Temporal Rule Engine (MITRE), is a method for predicting host status from microbiome time-series data, which achieves high accuracy while maintaining interpretability by learning predictive rules over automatically inferred time-periods and phylogenetically related microbes.