During the last 30 years, people have tried to communicate in an oral form with the computers, developing for this end an important amount of automatic speech recognition algorithms. Because of this, software such as the Dragon Dictate and the IBM Via Voice are already available to interact easily with the computer in oral form. However, during the last several years ASR has not reported important advances, not only due to the advances obtained until now, but also because the scientific community working in this area does not have founded another tool so powerful as HMM, despite a great number of alternatives that have been proposed since HMM appeared. This chapter presents the main elements required to create a practical ASR using HMM. The basic principles of the continuous density hidden Markov models (CDHMM) are also given.