Mask-face detection has been a significant task since the outbreak of the COVID-19 pandemic in early 2020. While various reviews on mask-face detection techniques up to 2021 are available, little has been reviewed on the distinction between two-class (i.e., wearing mask and without mask) and three-class masking, which includes an additional incorrect-mask-wearing class. Moreover, no formal review has been conducted on the techniques of implementing mask detection models in hardware systems or mobile devices. The objectives of this paper are three-fold. First, we aimed to provide an up-to-date review of recent mask-face detection research in both two-class cases and three-class cases, next, to fill the gap left by existing reviews by providing a formal review of mask-face detection hardware systems; and to propose a new framework named Out-of-distribution Mask (OOD-Mask) to perform the three-class detection task using only two-class training data. This was achieved by treating the incorrect-mask-wearing scenario as an anomaly, leading to reasonable performance in the absence of training data of the third class.