This paper presents a non--technical account of the developments in tree--based methods for the analysis of survival data with censoring. This review describes the initial developments, which mainly extended the existing basic tree methodologies to censored data as well as to more recent work. We also cover more complex models, more specialized methods, and more specific problems such as multivariate data, the use of time--varying covariates, discrete--scale survival data, and ensemble methods applied to survival trees. A data example is used to illustrate some methods that are implemented in R.