In recent years, there has been an increased focus on early detection, prevention, and prediction of diseases. This, together with advances in sensor technology and the Internet of Things, has led to accelerated efforts in the development of personal health monitoring systems. Semantic technologies have emerged as an effective way to not only deal with the issue of interoperability associated with heterogeneous health sensor data, but also to represent expert health knowledge to support complex reasoning required for decision-making. This study evaluates the state of the art in the use of semantic technologies in sensor-based personal health monitoring systems. Using a systematic approach, a total of 40 systems representing the state of the art in the field are analysed. Through this analysis, six key challenges that such systems must overcome for optimal and effective health monitoring are identified: interoperability, context awareness, situation detection, situation prediction, decision support, and uncertainty handling. The study critically evaluates the extent to which these systems incorporate semantic technologies to deal with these challenges and identifies the prominent architectures, system development and evaluation methodologies that are used. The study provides a comprehensive mapping of the field, identifies inadequacies in the state of the art, and provides recommendations for future research directions.