Bayesian inference is now routinely used in phylogenomics and, more generally, in macro-evolutionary studies. Beyond the philosophical debates it has raised concerning the choice of the prior and the meaning of posterior probabilities, Bayesian inference, combined with generic Monte Carlo algorithms, offers a flexible framework for introducing subjective or context information through the prior, but also, for designing hierarchical models formalizing complex patterns of variation (across sites or branches) or the integration of multiple levels of evolutionary processes. In this chapter, the principles of Bayesian inference, such as applied to phylogenetic reconstruction , are first introduced, with an emphasis on the key features of the Bayesian paradigm that explain its flexibility in terms of model design and its robustness in inferring complex patterns and processes. A more specific focus is then put on the question of modeling pattern-heterogeneity across sites, using both parametric and non-parametric random-effect models. Finally, the current computational challenges are discussed.