We give critical attention to the assumptions underlying Mendelian randomization analysis and their biological plausibility. Several scenarios violating the Mendelian randomization assumptions are described, including settings with inadequate phenotype definition, the setting of time-varying exposures, the presence of gene-environment interaction, the existence of measurement error, the possibility of reverse causation, and the presence of linkage disequilibrium. Data analysis examples are given, illustrating that the inappropriate use of instrumental variable techniques when the Mendelian randomization assumptions are violated can lead to biases of enormous magnitude. To help address some of the strong assumptions being made, three possible approaches are suggested. First, the original proposal of Katan (Lancet. 1986;1:507-508) for Mendelian randomization was not to use instrumental variable techniques to obtain estimates but merely to examine genotype-outcome associations to test for the presence of an effect of the exposure on the outcome. We show that this more modest goal and approach can circumvent many, though not all, the potential biases described. Second, we discuss the use of sensitivity analysis in evaluating the consequences of violations in the assumptions and in attempting to correct for those violations. Third, we suggest that a focus on negative, rather than positive, Mendelian randomization results may turn out to be more reliable.