Conversational Machine Comprehension (CMC), a research track in conversational AI, expects the machine to understand an open-domain natural language text and thereafter engage in a multi-turn conversation to answer questions related to the text. While most of the research in Machine Reading Comprehension (MRC) revolves around single-turn question answering (QA), multi-turn CMC has recently gained prominence, thanks to the advancement in natural language understanding via neural language models such as BERT and the introduction of large-scale conversational datasets such as CoQA and QuAC. The rise in interest has, however, led to a flurry of concurrent publications, each with a different yet structurally similar modeling approach and an inconsistent view of the surrounding literature. With the volume of model submissions to conversational datasets increasing every year, there exists a need to consolidate the scattered knowledge in this domain to streamline future research. This literature review attempts at providing a holistic overview of CMC with an emphasis on the common trends across recently published models, specifically in their approach to tackling conversational history. The review synthesizes a generic framework for CMC models while highlighting the differences in recent approaches and intends to serve as a compendium of CMC for future researchers.