Since falls are a major public health problem among older people, the number of systems aimed at detecting them has increased dramatically over recent years. This work presents an extensive literature review of fall detection systems, including comparisons among various kinds of studies. It aims to serve as a reference for both clinicians and biomedical engineers planning or conducting field investigations. Challenges, issues and trends in fall detection have been identified after the reviewing work. The number of studies using context-aware techniques is still increasing but there is a new trend towards the integration of fall detection into smartphones as well as the use of machine learning methods in the detection algorithm. We have also identified challenges regarding performance under real-life conditions, usability, and user acceptance as well as issues related to power consumption, real-time operations, sensing limitations, privacy and record of real-life falls.