Industry 4.0 concept has become a worldwide revolution that has been mainly led by the manufacturing sector. Continuous Process Industry is part of this global trend where there are aspects of the “fourth industrial revolution” that must be adapted to the particular context and needs of big continuous processes such as oil refineries that have evolved to control paradigms supported by sector-specific technologies where big volumes of operation-driven data are continuously captured from a plethora of sensors. The introduction of Artificial Intelligence techniques can overcome the current limitations of Advanced Control Systems (mainly MPCs) by providing better performance on highly non-linear and complex systems and by operating with a broader scope in terms of signals/data and sub-systems. Moreover, the state of the art of traditional PID/MPC based solutions is showing an asymptotic improvement that requires a disruptive approach in order to reach relevant improvements in terms of efficiency, optimization, maintenance, etc. This paper shows the key aspects in oil refineries to successfully adopt Big Data and Machine Learning solutions that can significantly improve the efficiency and competitiveness of continuous processes.