Summary Multiple imputation is now a well-established technique for analysing data sets where some units have incomplete observations. Provided that the imputation model is correct, the resulting estimates are consistent. An alternative, weighting by the inverse probability of observing complete data on a unit, is conceptually simple and involves fewer modelling assumptions, but it is known to be both inefficient (relative to a fully parametric approach) and sensitive to the choice of weighting model. Over the last decade, there has been a considerable body of theoretical work to improve the performance of inverse probability weighting, leading to the development of ‘doubly robust’ or ‘doubly protected’ estimators. We present an intuitive review of these developments and contrast these estimators with multiple imputation from both a theoretical and a practical viewpoint.