The availability of firm level data in international trade started a very quickly developing theoretical literature that focused on the micro evidence and understanding its implications for aggregate productivity and welfare. The new models were dealing with individual firm characteristics determining entry and exit from foreign markets and the different ways in which firms chose to enter. Two of the main features of this literature are that firms have heterogeneous productivities and need to pay a fixed costs in order to enter both their home and foreign markets. As a result, some do not find it optimal to export and it is those with higher productivity that do. This thesis is comprised of three theoretical papers (chapters) in which the models are with firms with heterogeneous productivities and there is steady state economic growth. The purpose in all three papers has been to generate results that are already established empirical facts but that have not been incorporated in the theoretical trade and growth literature. / Diss. Stockholm : Handelshögskolan i Stockholm, 2011