Boltzmann distribution in physics, Gibbs measure in mathematics, exponential family distributions in statistics, undirected graphical models in computer science, or energy-based models in machine learning — all these notions refer to the same general concept, also known as Markov Random Fields (MRFs). A recurrent interest for MRFs in many different branches of science is explained by the fact that they serve as a natural and interpretable modeling foundation for many scientific applications: MRFs have been used for modeling of natural systems at equilibrium since the creation of statistical physics! Yet, unknown training algorithms, as well as the lack of tools for generating predictions from these models presented the main barriers to the widespread use of MRFs in Scientific Machine Learning. In this talk, we review the state-of-the-art for learning of MRFs from data, and for constructing MRFs in forms which allow for an efficient generation of predictions and sampling. We illustrate a wide applicability of this concept in several distinct scientific areas: random graph models, statistical and quantum mechanical models, and field theories.