The death of an individual is not a repetitive event, so if a cause of death overtakes another cause in producing death, mortality rates from the overtaken cause decrease. This phenomenon is known as competing risks of death and it must be taken into account in any cause-specific mortality analysis. In this work the competing risks concept is formalized and some historical data are described. The main parametric tools to analyze competing risks are displayed, with a special look at the Gompertz and Weibull functions. Regarding non-parametric models, the Chiang method is shown and its applicability on both dependent and independent causes of death is discussed. Finally, other tools specially useful in clinical epidemiology are enumerated, including Cox regression, Kaplan-Meier and log-rank methods, as well as the interactions between competing risks and misclassification and selection biases.