Fetal phonocardiography (fPCG) is receiving attention as it is a promising method for continuous fetal monitoring due to its non-invasive and passive nature. However, it suffers from the interference from various sources, overlapping the desired signal in the time and frequency domains. This paper introduces the state-of-the-art methods used for fPCG signal extraction and processing, as well as means of detection and classification of various features defining fetal health state. It also provides an extensive summary of remaining challenges, along with the practical insights and suggestions for the future research directions.