Genome wide association studies (GWAS) have been very successful over the last decade at identifying genetic variants associated with disease phenotypes. However, interpretation of the results obtained can be challenging. Incorporation of further relevant biological measurements (e.g. 'omics' data) measured in the same individuals for whom we have genotype and phenotype data may help us to learn more about the mechanism and pathways through which causal genetic variants affect disease. We review various methods for causal inference that can be used for assessing the relationships between genetic variables, other biological measures, and phenotypic outcome, and present a simulation study assessing the performance of the methods under different conditions. In general, the methods we considered did well at inferring the causal structure for data simulated under simple scenarios. However, the presence of an unknown and unmeasured common environmental effect could lead to spurious inferences, with the methods we considered displaying varying degrees of robustness to this confounder. The use of causal inference techniques to integrate omics and GWAS data has the potential to improve biological understanding of the pathways leading to disease. Our study demonstrates the suitability of various methods for performing causal inference under several biologically plausible scenarios.