We investigate whether the gravity model (GM) can explain the statistical properties of the International Trade Network (ITN). We fit data on trade flows with a GM using alternative estimation techniques and we build GM-based predictions for the weighted topological properties of the ITN, which are then compared to the observed ones. Our exercises show that the GM: (i) may replicate part of the weighted-network structure only if the observed binary architecture is kept fixed; (ii) is not able to explain higher-order statistics that, like clustering, require the knowledge of triadic link-weight topological patterns, even if the binary structure perfectly replicates the observed one; (iii) performs very badly when asked to predict the presence of a link, or the level of the trade flow it carries, whenever the binary structure must be simultaneously estimated. Copyright Springer-Verlag Berlin Heidelberg 2013