This article is intended to serve as an introduction to the field of statistical SLU, based on the mainstream statistical modeling approach that shares a similar mathematical framework with many other statistical pattern recognition applications such as speech recognition. In particular, we formulated a number of statistical models for SLU in the literature as extensions to HMMs as segment models, where a multiple-word block (segment) with word dependency is generated from each underlying Markov state corresponding to each individual semantic slot defined from the application domain. In the past, due partly to its nature of symbolic rather than numeric processing, the important field of SLU in human language technology has not been widely exposed to the signal processing research community. However, many key techniques in SLU originated from statistical signal processing. And because SLU is becoming increasingly important, as one major target application area of ASR that has been dear to many signal processing researchers, we contribute this article to provide a natural bridge between ASR and SLU in methodological and mathematical foundation. It is our hope that when the mathematical basis of SLU becomes well known through this introductory article, more powerful techniques established by signal processing researchers may further advance SLU to form a solid application area, making speech technology a successful component for intelligent human-machine communication.