In recent years, cardiovascular diseases are on the rise, and they entail enormous health burdens on global economies. Cardiac vibrations yield a wide and rich spectrum of essential information regarding the functioning of the heart, and thus it is necessary to take advantage of this data to better monitor cardiac health by way of prevention in early stages. Specifically, seismocardiography (SCG) is a noninvasive technique that can record cardiac vibrations by using new cutting-edge devices as accelerometers. Therefore, providing new and reliable data regarding advancements in the field of SCG, i.e., new devices and tools, is necessary to outperform the current understanding of the State-of-the-Art (SoTA). This paper reviews the SoTA on SCG and concentrates on three critical aspects of the SCG approach, i.e., on the acquisition, annotation, and its current applications. Moreover, this comprehensive overview also presents a detailed summary of recent advancements in SCG, such as the adoption of new techniques based on the artificial intelligence field, e.g., machine learning, deep learning, artificial neural networks, and fuzzy logic. Finally, a discussion on the open issues and future investigations regarding the topic is included.