Distraction, misjudgement and driving mistakes can significantly affect a driver, resulting in an increased risk of accidents. There are diverse factors that can cause mistakes in driving such as unfamiliarity with the road, situation unawareness, fatigue, stress, and drowsiness. In emerging smart cars, sensing, actuation, advanced signal processing and machine learning are deployed to reduce the impact of driving errors by monitoring the state of the driver in real-time, detecting the mistakes, and deploying necessary actions to counteract them. Such strategies are collectively known as human-machine shared driving. Towards a better understanding of the developments taken place in this domain, as well as identifying gaps and trends in this discipline, a systematic review of the major studies and developments reported in the literature is conducted. The study is based on 155 papers of human-machine shared driving, selected through a thorough and comprehensive search of the literature.