The three chapters of this dissertation discuss what role complexity plays in different fields of international economics. First, we discuss the role of complex information in decision making of multinational companies. On the one hand, we test the hypotheses by Oldenski (2012) that affiliate sales are less likely if production process involves complex information. On the other hand, we test the hypothesis by Keller and Yeaple (2013) that the force of gravity is stronger in more complex sectors. We find support for the hypotheses in Oldenski and contradict the hypothesis in Keller and Yeaple. In the next chapter we test whether technological catch-up is slower in tacit knowledge intensive sectors. We also examine whether catch-up is slower in sectors with a large skill intensity and a high degree of export sophistication. Employing data between 1960 and 2000 covering manufacturing sectors, we find that catch-up is slower in more tacit knowledge intensive sectors, as well as in skill intensive and export sophisticated sectors. With more recent GTAP-data from 1997 to 2011 we find instead that catch-up is faster in more tacit knowledge intensive manufacturing sectors, whereas catch-up is slower in more tacit knowledge intensive services sectors. In the last chapter we take a closer look at the export sophistication of country's exports and it's effect in the growth regressions. We analyze whether within or between sector specialization in sophisticated goods matters more for economic growth and find that both are similarly important. Then we study export specialization within sectors across different products. Here we look into determinants of sectoral EXPYs, convergence and effect on aggregate economic growth. Finally, we decompose the EXPY measure into an absolute advantage and a market potential component to find that export sophistication driven by absolute advantage is what matters for economic growth.