Inertial Measurement Units (IMUs) are frequently implemented in wearable devices. Thanks to advances in signal processing and machine learning, applications of IMUs are not limited to those explicitly addressing body movements such as Activity Recognition (AR). On the other hand, wearing IMUs on the chest offers a few advantages over other body positions. AR and posture analysis, cardiopulmonary parameters estimation, voice and swallowing activity detection and other measurements can be approached through chest-worn inertial sensors. This survey tries to introduce the applications that come with the chest-worn IMUs and summarizes the existing methods, current challenges and future directions associated with them. In this regard, this paper references a total number of 57 relevant studies from the last 10 years and categorizes them into seven application areas. We discuss the inertial sensors used as well as their placement on the body and their associated validation methods based on the application categories. Our investigations show meaningful correlations among the studies within the same application categories. Then, we investigate the data processing architectures of the studies from the hardware point of view, indicating a lack of effort on handling the main processing through on-body units. Finally, we propose combining the discussed applications in a single platform, finding robust ways for artifact cancellation, and planning optimized sensing/processing architectures for them, to be taken more seriously in future research.