Accidental falls have become one of the most frequent general health issues in recent years due to the rate of occurrence. Individuals aged above 65 are more prone to accidental falls. Accidental falls result in severe injuries such as concussion, head trauma, physical disabilities even to deaths in serious cases if the patients are not rescued in time. Thus, researchers are focusing on developing fall detection systems that facilitate the detection and quick rescue of fall victims. The smartphone-based fall detection systems use various built-in sensors of smartphones mostly Tri-axial accelerometer, magnetometer, gyroscope, and camera. The majority of the systems employ threshold based algorithms (TBA). Some systems use machine learning (ML) based algorithms or a combination of ML and TBA based algorithms to detect falls. Each of these types of systems has its trade-offs. The goal of this paper is to review fall detection systems based on data from smartphone sensors that employ either one of TBA, ML or combination of both. We also present the taxonomy based on systematic comparisons of existing studies for smartphone-based fall detection solutions.