A common feature of many failure time data in epidemiological studies or reliability studies is that they are simultaneously censored and truncated. In this talk we explore the case of arbitrarily censored and truncated data and the estimation of parameters involved. We consider the nonparametric case, where the parameter of interest is the survival function or the density probability function, as well as the parametric or semiparametric case where the parameter of interest is a finite dimensional vector of regression parameters. Passing through the widely used in survival analysis Cox model of proportional hazards, we deal with the nonproportional hazards case based on frailty models. We illustrate our theory with a real data set related to AIDS.