There has been a trend of moving from simply de-identification to providing extended data control to their owner (e.g., data portability, and right to be forgotten), partly due to the introduction of the General Data Protection Regulation (GDPR). Hence, in this paper we survey the literature to provide an in-depth understanding of the existing approaches for personal data control (e.g., we observe that most existing approaches are generally designed to facilitate compliance), as well as the privacy regulations in Europe, United Kingdom, California, South Korea, and Japan. Based on the review, we identify the associated technical requirements, as well as a number of research gaps and potential future directions (e.g., the need for transparent processing of personal data and establishment of clear procedure in ensuring personal data control).