This chapter reviews in detail our network gravity model (Garcia-Perez et al., 2016b), a new approach to predict both the existence and the volume of significant trade interactions between pairs of countries in the world based on methodologies and reverse engineering techniques from Network Science (Newman, 2010; Cohen and Havlin, 2010). The network gravity model relies on economic sizes and on effective distances that incorporate the different dimensions affecting international trade—including but not limited to geog- raphy—implicitly encoded on the complex patterns of trade interactions. We describe a pure geometric counterpart using hyperbolic space, which has been conjectured to be the natural geometry underlying complex networks (Bogunáet al., 2009; Krioukov et al., 2010; Papadopoulos et al., 2012; Borassi et al., 2015). In the hyperbolic trade space, economic sizes and geographical distances are combined into a sole distance metric as a proxy of aggregate trade barriers, such that the closer countries are in hyperbolic trade space, the greater their chance of being connected. We estimate trade distances from empirical data to represent the WTW through World Trade Maps. The maps are annual and cover a time span of fourteen decades. The collection as a whole is referred to as the World Trade Atlas 1870-2013. We also extended the network gravity model to deal with trade flows such that the same underlying metric space can explain simultaneously the existence and the volume of trade interactions (Allard et al., 2017).