The purpose of this paper is to provide an up-to-date treatment of advanced analytic, state-space based techniques to study dependability models with non-exponential distributions. We first provide an overview of different techniques for the solution of non-Markovian state-space based models, including phase-type expansion and a general framework which allows us to deal with renewal, semi-Markov, and Markov-regenerative processes, trying to characterize them on dependability contexts. In the last part of the paper, we illustrate these techniques by means of some examples dealing with common non-exponential reliability behaviors. Our aim is to provide a reference for practising engineers, researchers, and students in state-space dependability modeling and evaluation. Copyright © 2012 John Wiley & Sons, Ltd.