The explosive growth and widespread accessibility of medical information on the Internet have led to a surge of research activity in a wide range of scientific communities including health informatics and information retrieval (IR). One of the common concerns of this research, across these disciplines, is how to design either clinical decision support systems or medical search engines capable of providing adequate support for both novices (e.g., patients and their next-of-kin) and experts (e.g., physicians, clinicians) tackling complex tasks (e.g., search for diagnosis, search for a treatment). However, despite the significant multi-disciplinary research advances, current medical search systems exhibit low levels of performance. This survey provides an overview of the state of the art in the disciplines of IR and health informatics, and bridging these disciplines shows how semantic search techniques can facilitate medical IR. First,we will give a broad picture of semantic search and medical IR and then highlight the major scientific challenges. Second, focusing on the semantic gap challenge, we will discuss representative state-of-the-art work related to feature-based as well as semantic-based representation and matching models that support medical search systems. In addition to seminal works, we will present recent works that rely on research advancements in deep learning. Third, we make a thorough cross-model analysis and provide some findings and lessons learned. Finally, we discuss some open issues and possible promising directions for future research trends.