Pharmacoepidemiological studies provide important information on the safety and effectiveness of medications, but the validity of study findings can be threatened by residual bias. Ideally, biases would be minimised through appropriate study design and statistical analysis methods. However, residual biases can remain, for example due to unmeasured confounders, measurement error, or selection into the study. A group of sensitivity analysis methods, termed quantitative bias analyses, are available to assess, quantitatively and transparently, the robustness of study results to these residual biases. These approaches include methods to quantify how the estimated effect would be altered under specified assumptions about the potential bias, and methods to calculate bounds on effect estimates. This article introduces quantitative bias analyses for unmeasured confounding, misclassification, and selection bias, with a focus on their relevance and application to pharmacoepidemiological studies.