The detection and segmentation of stained cells and nuclei are essential prerequisites for subsequent quantitative research for many diseases. Recently, deep learning has shown strong performance in many computer vision problems, including solutions for medical image analysis. Furthermore, accurate stereological quantification of microscopic structures in stained tissue sections plays a critical role in understanding human diseases and developing safe and effective treatments. In this article, we review the most recent deep learning approaches for cell (nuclei) detection and segmentation in cancer and Alzheimer's disease with an emphasis on deep learning approaches combined with unbiased stereology. Major challenges include accurate and reproducible cell detection and segmentation of microscopic images from stained sections. Finally, we discuss potential improvements and future trends in deep learning applied to cell detection and segmentation.