The last decade has shown an increasing interest on advanced driver assistance systems (ADAS) based on shared control, where automation is continuously supporting the driver at the control level with an adaptive authority. A first look at the literature offers two main research directions: 1) an ongoing effort to advance the theoretical comprehension of shared control, and 2) a diversity of automotive system applications with an increasing number of works in recent years. Yet, a global synthesis on these efforts is not available. To this end, this article covers the complete field of shared control in automated vehicles with an emphasis on these aspects: 1) concept, 2) categories, 3) algorithms, and 4) status of technology. Articles from the literature are classified in theory- and application-oriented contributions. From these, a clear distinction is found between coupled and uncoupled shared control. Also, model-based and model-free algorithms from these two categories are evaluated separately with a focus on systems using the steering wheel as the control interface. Model-based controllers tested by at least one real driver are tabulated to evaluate the performance of such systems. Results show that the inclusion of a driver model helps to reduce the conflicts at the steering. Also, variables such as driver state, driver effort, and safety indicators have a high impact on the calculation of the authority. Concerning the evaluation, driver-in-the-loop simulators are the most common platforms, with few works performed in real vehicles. Implementation in experimental vehicles is expected in the upcoming years.