Although initially introduced and studied in the late 1960s and early 1970s, statistical methods of Markov source or hidden Markov modeling have become increasingly popular in the last several years. There are two strong reasons why this has occurred. First the models are very rich in mathematical structure and hence can form the theoretical basis for use in a wide range of applications. Second the models, when applied properly, work very well in practice for several important applications. In this paper we attempt to carefully and methodically review the theoretical aspects of this type of statistical modeling and show how they have been applied to selected problems in machine recognition of speech.-Although　initially　introduced　and studied　in　the　late 1960s　and early　1970s, statistical　methods of Markov　source　or hidden　Markov modeling　have　become increasingly　popular　in　the　last　several years. There are　two strong reasons why this has　occurred. First the models are very rich in mathematical structure　and hence can form the　theoretical　basis　for　use in a wide range of applications.　Second the　models, when applied properly,　work very well in practice for　several　important applications.　In this paper we attempt to carefully　and methodically review　the theoretical　aspects of this type of statistical　modeling and show　how they　have　been　applied　to selected problems in machine recognition　of speech.