Digital pathology and microscopy image analysis is widely used for comprehensive studies of cell morphology or tissue structure. Manual assessment is labor intensive and prone to interobserver variations. Computer-aided methods, which can significantly improve the objectivity and reproducibility, have attracted a great deal of interest in recent literature. Among the pipeline of building a computer-aided diagnosis system, nucleus or cell detection and segmentation play a very important role to describe the molecular morphological information. In the past few decades, many efforts have been devoted to automated nucleus/cell detection and segmentation. In this review, we provide a comprehensive summary of the recent state-of-the-art nucleus/cell segmentation approaches on different types of microscopy images including bright-field, phase-contrast, differential interference contrast, fluorescence, and electron microscopies. In addition, we discuss the challenges for the current methods and the potential future work of nucleus/cell detection and segmentation.