After Tiebout’s seminal paper, a stream of literature emerged that studies the location choice behaviour of households. In the last two decades, the models developed generalised conventional hedonic analyses by studying house prices in a coherent empirical framework that incorporates heterogeneity among households and neighbourhoods. They offer new possibilities to study location choice in equilibrium with public goods in the Tiebout tradition. Moreover, they generalise the monocentric model of urban economics. This paper discusses these sorting models. Although the focus is on the policy-relevant questions that can be addressed by this approach, we pay due attention to the economic content of the models, and to some important econometric issues involved. An important feature of the sorting framework that we emphasise throughout the paper is that it allows one to study the impact of local amenities in a rigorous setting that allows for the computation of welfare measures, notably the willingness-to-pay of various groups for specific amenities. In the international literature, schools are the most intensively studied example, but other amenities, such as the presence of parks and ‘consumer city’ amenities, such as restaurants, cinemas and theatres can also be studied in this framework. The structural modelling of the impact of amenities by sorting models allows for policy simulations, in which the general equilibrium impact of changes in the value of these amenities can be analysed through counterfactual analysis.