In the analysis of time-to-event data, competing risks occur when multiple event types are possible, and the occurrence of a competing event precludes the occurrence of the event of interest. In this situation, statistical methods that ignore competing risks can result in biased inference regarding the event of interest. We review the mechanisms that lead to bias, and describe several statistical methods that have been proposed to avoid bias by formally accounting for competing risks in the analyses of the event of interest. Through simulation, we illustrate that Gray's test should be used in lieu of the logrank test for non-parametric hypothesis testing. We also compare the two most popular models for semi-parametric modelling: the cause-specific hazards (CSH) model and Fine-Gray (F-G) model. We explain how to interpret estimates obtained from each model, and identify conditions under which the estimates of the hazard ratio and subhazard ratio differ numerically. Finally, we evaluate several model diagnostic methods with respect to their sensitivity to detect lack-of-fit when the CSH model holds, but the F-G model is misspecified and vice versa.