Mortality models that can interpret the observed data well with reasonable biological/physiological mechanism are always desirable. Attempts along this direction of mortality modelling have been made. We propose to model a hypothetical aging process by a finite-state continuous-time Markov process with a single absorbing state. Under this model, the time-till-death random variable follows a phase-type distribution. The model possesses many desirable analytical properties that are useful for mortality analysis. Very recently, we extend the model to incorporate stochastic mortality by adding a subordinating process. The desirable properties of the model enable us to derive many quantities of interest such as the distribution of future survival rates, prediction intervals, the term structure of mortality as well as the value of caps and floors on the survival index analytically.