A realistically inserted virtual object in the real-time physical environment is a desirable feature in augmented reality (AR) applications and mixed reality (MR) in general. This problem is considered a vital research area in computer graphics, a field that is experiencing ongoing discovery. The algorithms and methods used to obtain dynamic and real-time illumination measurement, estimating, and rendering of augmented reality scenes are utilized in many applications to achieve a realistic perception by humans. We cannot deny the powerful impact of the continuous development of computer vision and machine learning techniques accompanied by the original computer graphics and image processing methods to provide a significant range of novel AR/MR techniques. These techniques include methods for light source acquisition through image-based lighting or sampling, registering and estimating the lighting conditions, and composition of global illumination. In this review, we discussed the pipeline stages with the details elaborated about the methods and techniques that contributed to the development of providing a photo-realistic rendering, visual coherence, and interactive real-time illumination results in AR/MR.