International Trade (IT) plays a fundamental role in today's economy: by connecting world countries production and consumption processes, it radically contributes in shaping their economy and development path. Although its evolving structure and determinants have been widely analyzed in the literature, much less has been done to understand its interplay with other complex phenomena. The aim of this work is, precisely in this direction, to study the relations of IT with International Migration (IM) and Foreign Direct Investments (FDI). In both cases the procedure used is to first approach the problem in a multiple-networks perspective and than deepen the analysis by using ad hoc econometrics techniques. With respect to IM, a general positive correlation with IT is highlighted and product categories for which this effect is stronger are identified and cross-checked with previous classifications. Next, employing spatial econometric techniques and proposing a new way to define country neighbors based on the most intense IM flows, direct/indirect network effects are studied and a stronger competitive effect of third country migrants is identified for a specific product class. In the case of FDI, first correlations between the two networks are identified, highlighting how they can be mostly explained by countries economic/demographic size and geographical distance. Then, using the Heckman selection model with a gravity equation, (non-linear) components arising from distance, position in the Global Supply Chain and presence of Regional Trade Agreements are studied. Finally, it is shown how IT and FDI correlation changes with sectors: they are complements in manufacturing, but substitutes in services.