Coronary Heart Disease (CHD) is a leading cause of death in the modern world. The development of modern analytical tools for diagnostics and treatment of CHD is receiving substantial attention from the scientific community. Deep learning-based algorithms, such as segmentation networks and detectors, play an important role in assisting medical professionals by providing timely analysis of a patient's angiograms. This paper focuses on X-Ray Coronary Angiography (XCA), which is considered to be a "gold standard" in the diagnosis and treatment of CHD. First, we describe publicly available datasets of XCA images. Then, classical and modern techniques of image preprocessing are reviewed. In addition, common frame selection techniques are discussed, which are an important factor of input quality and thus model performance. In the following two chapters we discuss modern vessel segmentation and stenosis detection networks and, finally, open problems and current limitations of the current state-of-the-art.