Over the past twenty years, numerous research outcomes have been published, related to the design and implementation of soft sensors. In modern industrial processes, various types of soft sensors are used, which play essential roles in process monitoring, control and optimization. Emerging new theories, advanced techniques and the information infrastructure have enabled the elevation of the performance of soft sensing. However, novel opportunities are accompanied by novel challenges. This work is motivated by these observations and aims to present a comprehensive review of the developments since the start of the millennium. While a few books and review articles are published on the related topics, more focus on the most up-to-the-date advancement is put in this work, from the perspective of systems and control.