Since the early 1990s many empirical studies have been conducted on the impact of international migration on international trade, predominantly from the host country perspective. Because most studies have adopted broadly the same specification, namely a log-linear gravity model of export and import flows augmented with the logarithm of the stock of immigrants from specific source countries as an additional explanatory variable, the resulting elasticities are broadly comparable and yield a set of estimates that is well suited to meta-analysis. We therefore compile and analyze in this paper the distribution of immigration elasticities of imports and exports across 48 studies that yielded 300 observations. The results show that immigration complements rather than substitutes for trade flows between host and origin countries. Correcting for heterogeneity and publication bias, an increase in the number of immigrants by 10 percent may be expected to increase the volume of trade on average by about 1.5 percent. However, the impact is lower for trade in homogeneous goods. Over time, the growing stock of immigrants decreases the elasticities. The estimates are affected by the choice of some covariates, the nature of the data (cross-section or panel) and the estimation technique. Elasticities vary between countries in ways that cannot be fully explained by study characteristics; trade restrictions and immigration policies matter for the impact of immigration on trade. The migrant elasticity of imports is larger than that of exports in about half the countries considered, but the publication bias and heterogeneity-corrected elasticity is slightly larger for exports than for imports.