Mendelian Randomization (MR) uses genetic variants as instrumental variables (IVs) to estimate the causal effects of modifiable exposures on outcomes. The core conditions required for a genetic variant to identify a causal effect are that it 1) is associated with the exposure, 2) has no direct pathway between it and the outcome, and 3) is not associated with any unobserved confounding variables. In practice, individual genetic variants are only weakly associated with exposures so that we would obtain biased estimates, even if the core conditions were satisfied. This has led researchers to consider the use of multiple genetic variants in their analyses. However, even here, the impact of pleiotropy, and other problems such as linkage disequilibrium and population stratification, can lead to bias through failure of core conditions 2) and 3). In this paper, we compare two recently developed methods, Egger regression and median regression, which are claimed to be robust to invalid IVs and which have been applied by other researchers. We also investigate the performance of another new method, sisVIVE, which has good theoretical properties but is much less widely used. We discuss the relative performance of these methods through simulation experiments and an application to estimate the causal effect of BMI on social outcomes using genetic data from Understanding Society.