It is now clear that semi-Markov processes play an increasingly crucial role in business and industry; this is partially due to the fact that, with the powerful mathematical software now existing, the numerical treatment of basic integral equations is easier and so leads to more concrete applications; moreover the development of topics such as non-homogeneous models and statistical estimation make it possible to construct more adequate models of real-life problems and to calibrate the basic parameters of the models more accurately from real data. This book presents many models that are or could be useful for applications in real-life problems. The editor hopes that it will contribute to the stimulation of new interactions between the theoretical development and the applications of semi-Markov models.