Genome‐wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual‐level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse‐variance weighted average of variant‐specific associations and a likelihood‐based approach for summarized data give similar estimates and precision to the two‐stage least squares method for individual‐level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the P‐value in a linear regression of the risk factor for each variant is less than , then weak instrument bias will be small. We use these methods to estimate the causal association of low‐density lipoprotein cholesterol (LDL‐C) on coronary artery disease using published data on five genetic variants. A 30% reduction in LDL‐C is estimated to reduce coronary artery disease risk by 67% (95% CI: 54% to 76%). We conclude that Mendelian randomization investigations using summarized data from uncorrelated variants are similarly efficient to those using individual‐level data, although the necessary assumptions cannot be so fully assessed.