Genetic association analyses often involve data from multiple potentially-heterogeneous subgroups. The expected amount of heterogeneity can vary from modest (e.g. a typical meta-analysis), to large (e.g. a strong gene-environment interaction). However, existing statistical tools are limited in their ability to address such heterogeneity. Indeed, most genetic association meta-analyses use a "fixed effects" analysis, which assumes no heterogeneity. Here we develop and apply Bayesian association methods to address this problem. These methods are easy to apply (in the simplest case, requiring only a point estimate for the genetic effect, and its standard error, from each subgroup), and effectively include standard frequentist meta-analysis methods, including the usual "fixed effects" analysis, as special cases. We apply these tools to two large genetic association studies: one a meta-analysis of genome-wide association studies from the Global Lipids consortium, and the second a cross-population analysis for expression quantitative trait loci (eQTLs). In the Global Lipids data we find, perhaps surprisingly, that effects are generally quite homogeneous across studies. In the eQTL study we find that eQTLs are generally shared among different continental groups, and discuss consequences of this for study design.