Missing data in covariates are known to result in biased estimates of association with the outcome and loss of power to detect associations. Missing data can also lead to other challenges in time-to-event analyses including the handling of time-varying effects of covariates, selection of covariates and their flexible modelling. This review aimed to understand how researchers are approaching time-to-event analyses when missing data are present. Medline and Embase were searched for observational time-to-event studies published from January 2011 to January 2018. We assessed the covariate selection procedure, assumptions of proportional hazards models, if functional forms were considered and how missing data affected this. We recorded the extent of missing data and how it was addressed in the analysis, for example using a complete-case analysis or multiple imputation. 148 studies were included in the review. On average, 15% of data were discarded due to missingness while determining the study population and 32% during the analysis stage. In total, 86% did not state any missing data assumptions. Complete-case analysis was common (56%) while 22% used multiple imputation.