Object pose detection and tracking has recently attracted increasing attention due to its wide applications in many areas, such as autonomous driving, robotics, and augmented reality. Among methods for object pose detection and tracking, deep learning is the most promising one that has shown better performance than others. However, there is lack of survey study about latest development of deep learning based methods. Therefore, this paper presents a comprehensive review of recent progress in object pose detection and tracking that belongs to the deep learning technical route. To achieve a more thorough introduction, the scope of this paper is limited to methods taking monocular RGB/RGBD data as input, covering three kinds of major tasks: instance-level monocular object pose detection, category-level monocular object pose detection, and monocular object pose tracking. In our work, metrics, datasets, and methods about both detection and tracking are presented in detail. Comparative results of current state-of-the-art methods on several publicly available datasets are also presented, together with insightful observations and inspiring future research directions.