Representational models specify how complex patterns of neural activity relate to visual stimuli, motor actions, or abstract thoughts. Here we review pattern component modeling (PCM), a practical Bayesian approach for evaluating such models. Similar to encoding models, PCM evaluates the ability of models to predict novel brain activity patterns. In contrast to encoding models, however, the activity of individual voxels across conditions (activity profiles) are not directly fitted. Rather, PCM integrates over all possible activity profiles and computes the marginal likelihood of the data under the activity profile distribution specified by the representational model. By using an analytical expression for the marginal likelihood, PCM allows the fitting of flexible representational models, in which the relative strength and form of the encoded feature spaces can be estimated from the data. We present here a number of different ways in which such flexible representational models can be specified, and how models of different complexity can be compared. We then provide a number of practical examples from our recent work in motor control, ranging from fixed models to more complex non-linear models of brain representations. The code for the fitting and cross-validation of representational models is provided in an open-source software toolbox.