Driver behaviour monitoring is a broad area of research, with a variety of methods and approaches. Distraction from the use of electronic devices, such as smartphones for texting or talking on the phone, is one of the leading causes of vehicle accidents. With the increasing number of sensors available in vehicles, there is an abundance of data available to monitor driver behaviour, but it has only been available to vehicle manufacturers and, to a limited extent, through proprietary solutions. Recently, research and practice have shifted the paradigm to the use of smartphones for driver monitoring and have fuelled efforts to support driving safety. This systematic review paper extends a preliminary, previously carried out author-centric literature review on smartphone-based driver monitoring approaches using snowballing search methods to illustrate the opportunities in using smartphones for driver distraction detection. Specifically, the paper reviews smartphone-based approaches to distracted driving behaviour detection, the smartphone sensors and detection methods applied, and the results obtained.