Distracted driving is known to be one of the leading causes of vehicle accidents. With the increase in the number of sensors available within vehicles, there exists an abundance of data for monitoring driver behaviour, which, however, have so far only been comparable across vehicle manufacturers to a limited extent due to proprietary solutions. A special role in distraction is played by the smartphone, which is repeatedly a source of distraction for drivers through calls and messages. However, the smartphone can be used for driver behaviour monitoring (like driver distraction detection) too, as current developments show. As vehicle manufacturer-independent device, which is usually equipped with adequate sensor technology, smartphones can provide significant advantages, however, an overview of such approaches is missing so far. Thus, this work carries out an author-centric literature review of 16 research papers to illustrate the opportunities in using smartphones to detect driver distraction.