Computerized microscopy image analysis plays an important role in computer aided diagnosis and prognosis. Machine learning techniques have powered many aspects of medical investigation and clinical practice. Recently, deep learning is emerging as a leading machine learning tool in computer vision and has attracted considerable attention in biomedical image analysis. In this paper, we provide a snapshot of this fast-growing field, specifically for microscopy image analysis. We briefly introduce the popular deep neural networks and summarize current deep learning achievements in various tasks, such as detection, segmentation, and classification in microscopy image analysis. In particular, we explain the architectures and the principles of convolutional neural networks, fully convolutional networks, recurrent neural networks, stacked autoencoders, and deep belief networks, and interpret their formulations or modelings for specific tasks on various microscopy images. In addition, we discuss the open challenges and the potential trends of future research in microscopy image analysis using deep learning.