Deep learning has attracted great attention in the medical imaging community as a promising solution for automated, fast and accurate medical image analysis, which is mandatory for quality healthcare. Convolutional neural networks and its variants have become the most preferred and widely used deep learning models in medical image analysis. In this paper, concise overviews of the modern deep learning models applied in medical image analysis are provided and the key tasks performed by deep learning models, i.e. classification, segmentation, retrieval, detection, and registration are reviewed in detail. Some recent researches have shown that deep learning models can outperform medical experts in certain tasks. With the significant breakthroughs made by deep learning methods, it is expected that patients will soon be able to safely and conveniently interact with AI-based medical systems and such intelligent systems will actually improve patient healthcare. There are various complexities and challenges involved in deep learning-based medical image analysis, such as limited datasets. But researchers are actively working in this area to mitigate these challenges and further improve health care with AI.