Flexible brand choice models which are not restricted to linear deterministic utility functions offer a way to prevent biased estimates due to nonlinear effects of predictors. One type of flexible choice models approximates deterministic utility by a multilayer perceptron. We describe several variants of this model type which differ with respect to assumptions about error terms and heterogeneity of coefficients. After dealing with appropriate estimation methods, model evaluation criteria and tools for interpreting estimation results, we give an overview of studies applying such models to brand choice data.