One of the most frequently used concepts applied to a variety of engineering and scientific studies over the recent years is that of a Hidden Markov Model (HMM). The Hidden semi-Markov model (HsMM) is contrived in such a way that it does not make any premise of constant or geometric distributions of a state duration. In other words, it allows the stochastic process to be a semi-Markov chain. Each state can have a collection of observations and the duration of each state is a variable. This allows the HsMM to be used extensively over a range of applications. Some of the most prominent work is done in speech recognition, gene prediction, and character recognition. This thesis deals with the general structure and modeling of Hidden semi-Markov models and their implementations. It will further show the details of evaluation, decoding, and training with a running example.