This paper provides an overview of multiple imputation and current perspectives on its use in medical research. We begin with a brief review of the problem of handling missing data in general and place multiple imputation in this context, emphasizing its relevance for longitudinal clinical trials and observational studies with missing covariates. We outline how multiple imputation proceeds in practice and then sketch its rationale. We explore the problem of obtaining proper imputations in some detail and distinguish two main classes of approach, methods based on fully multivariate models, and those that iterate conditional univariate models. We show how the use of so-called uncongenial imputation models are particularly valuable for sensitivity analyses and also for certain analyses in clinical trial settings. We also touch upon other forms of sensitivity analysis that use multiple imputation. Finally, we give some open questions that the increasing use of multiple imputation has thrown up, which we believe are useful directions for future research.