The recent development in the areas of deep learning and deep convolutional neural networks has significantly progressed and advanced the field of computer vision (CV) and image analysis and understanding. Complex tasks such as classifying and segmenting medical images and localising and recognising objects of interest have become much less challenging. This progress has the potential of accelerating research and deployment of multitudes of medical applications that utilise CV. However, in reality, there are limited practical examples being physically deployed into front-line health facilities. In this paper, we examine the current state of the art in CV as applied to the medical domain. We discuss the main challenges in CV and intelligent data-driven medical applications and suggest future directions to accelerate research, development, and deployment of CV applications in health practices. First, we critically review existing literature in the CV domain that addresses complex vision tasks, including: medical image classification; shape and object recognition from images; and medical segmentation. Second, we present an in-depth discussion of the various challenges that are considered barriers to accelerating research, development, and deployment of intelligent CV methods in real-life medical applications and hospitals. Finally, we conclude by discussing future directions.