Pronunciation assessment and its application in computer-aided pronunciation training (CAPT) have seen impressive progress in recent years. With the rapid growth in language processing and deep learning over the past few years, there is a need for an updated review. In this paper, we review methods employed in pronunciation assessment for both phonemic and prosodic. We categorize the main challenges observed in prominent research trends, and highlight existing limitations, and available resources. This is followed by a discussion of the remaining challenges and possible directions for future work.