"Accounting for firms' heterogeneity in trade patterns is probably one of the key innovations of international trade that occurred during the last decade. The impact of initial papers such as Melitz (2003) and Bernard and Jensen (1999) is so large in the field that it is considered to have introduced a new paradigm. Apart from providing a convincing framework for a set of empirical facts, the main motivation of this literature was that there are new gains to be expected from trade liberalization. Those come from a selection process, raising aggregate productivity through the reallocation of output among heterogeneous firms. It initially seemed that the information requirements for trade policy evaluations had become much more demanding, in particular requiring detailed micro data. However, the recent work of Arkolakis et al. (2011) suggests that two aggregate ``sufficient statistics'' may be all that is needed to compute the welfare changes associated with trade liberalization. More, they show that those statistics are the same when evaluating welfare changes in representative firm models. The project has three parts. The first one starts by showing that the sufficient statistics approach relies crucially on a specific distributional assumption on heterogeneity, the Pareto distribution. When distributed non-Pareto, heterogeneity does matter, i.e. aggregate statistics are not sufficient to evaluate welfare changes and predict trade patterns. The second part of the project specifies which type of firm-level heterogeneity matters. It shows how to identify which sectors are characterized by ``productivity sorting'' and in which ones ``quality sorting'' is more relevant. Extending the analysis to multiple product firms, the third part shows that heterogeneity inside the firm also matters for welfare changes following trade shocks. It considers how the change in the product mix of the firm following trade liberalization alters the measured productivity of the firm."