The study examines various approaches oriented towards conceptual and numerical reduction of first-principle models, data-driven methodologies for surrogate (black box) and hybrid (grey box) modeling, and addresses the prospect of using digital twins in chemical and process engineering. In the case of numerical reduction of mechanistic models, special attention is paid to methodologies in which simulation data are used to construct light but robust numerical models while preserving all the physics of the problem, yielding reduced-order datadriven but still white-box models. In addition to reviewing various methodologies and identifying their applications in chemical engineering, including industrial process engineering, as well as fundamental research, the study outlines associated problems and challenges, as well as the risks posed by the era of big data.