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This article's goal is to provide an in-depth understanding of the principles of FSMC modeling of fading channels with its applications in wireless communication systems. While the emphasis is on frequency nonselective or flat-fading channels, this understanding will be useful for future generalizations of FSMC models for frequency-selective fading channels. The target audience of this article include both theory- and practice-oriented researchers who would like to design accurate channel models for evaluating the performance of wireless communication systems in the physical or media access control layers, or those who would like to develop more efficient and reliable transceivers that take advantage of the inherent memory in fading channels. Both FSMC models and flat-fading channels will be formally introduced. FSMC models are particulary suitable to represent and estimate the relatively fast flat-fading channel gain in each subcarrier.