It is widely acknowledged how the relentless surge of Volume, Velocity and Variety of data, as well as the simultaneous increase of computational resources have stimulated the development of data-driven methods with unprecedented flexibility and predictive power. However, not every environmental study entails a large data set: many applications ranging from astronomy or paleo-climatology have a high associated sampling cost and are instead well explained by physics-informed partial differential equations. Throughout the past few years, a new and powerful paradigm has emerged in the machine learning literature, merging data-driven and physics-informed problems, hence providing a unified framework for a whole spectrum of problems ranging from data-rich/context-poor to data-poor/context-rich. In this talk, I will present this new framework and discuss some of the most recent efforts to reformulate it as a stochastic model-based approach, thereby allowing calibrated uncertainty quantification.