In this chapter, we discuss mathematical models of automatic speech recognition (ASR), an important area of speech signal processing. It is a process of mapping an acoustic signal of speech into words or a sequence of words for further linguistic processing and speech understanding. Hands-free applications are everywhere nowadays, finding a restaurant or a book in speech production and transmission, statistical modeling tools are necessary for the task. In the following sections, we shall explain why Hidden Markov models (HMM) make good sense and how they are analyzed and trained to perform the recognition task in the case of isolated words. Matlab programs will be provided for demonstration of the computational aspects as a prime example of machine learning methodology at work. References for further reading and recent developments are also provided.