Recent trends on hybrid modeling for Industry 4.0

•Hybrid modeling has been attracting the interest of the scientific community for almost 30 years.•Big data and the industry 4.0 bring opportunities for new hybrid modeling solutions.•We review hybrid modeling schemes, their training, validation and applications.•Usually mechanistic models are improved by data-driven models.•There is the need for a generic framework balancing prior and data-driven knowledge. The chemical processing industry has relied on modeling techniques for process monitoring, control, diagnosis, optimization, and design, especially since the third industrial revolution and the emergence of Process Systems Engineering. The fourth industrial revolution, connected to massive digitization, made it possible to collect and process large volumes of data triggering the development of data-driven frameworks for knowledge extraction. However, one must not leave behind the successful solutions developed over decades based on first principle mechanistic modeling approaches. At present, both industry and researchers are realizing the need for new ways to incorporate process and phenomenological knowledge in big data and machine learning frameworks, leading to more robust and intelligible artificial intelligence solutions, capable of assisting the target stakeholders in their activities and decision processes. In this article, we review hybrid modeling techniques, associated system identification methodologies and model assessment criteria. Applications in chemical and biochemical processes are also referred.