Falls are a major cause of health and psychological problems as well as hospitalization costs among older adults. Thus, the investigation on automatic Fall Detection Systems (FDSs) has received special attention from the research community during the last decade. In this area, the widespread popularity, decreasing price, computing capabilities, built-in sensors and multiplicity of wireless interfaces of Android-based devices (especially smartphones) have fostered the adoption of this technology to deploy wearable and inexpensive architectures for fall detection. This paper presents a critical and thorough analysis of those existing fall detection systems that are based on Android devices. The review systematically classifies and compares the proposals of the literature taking into account different criteria such as the system architecture, the employed sensors, the detection algorithm or the response in case of a fall alarms. The study emphasizes the analysis of the evaluation methods that are employed to assess the effectiveness of the detection process. The review reveals the complete lack of a reference framework to validate and compare the proposals. In addition, the study also shows that most research works do not evaluate the actual applicability of the Android devices (with limited battery and computing resources) to fall detection solutions.