In this chapter, we introduce probabilistic models of the mechanisms that generate data. Probabilistic models let us express scientific hypotheses with clear truth conditions, even when the mechanisms are inherently stochastic. A conditional probabilistic model describes how the conditional probability density of a response variable given a predictor depends on the predictor’s value. This dependence is controlled by a parameter vector, whose possible values form the model’s hypothesis space. Fitting the model means choosing a specific parameter vector based on data. One common approach is maximum likelihood, which selects parameters that make the observed data most probable. For many conditional models, maximising likelihood is equivalent to minimising the residual sum of squares.