  Statistical physics aims to describe properties of macroscale systems in
terms of distributions of their microscale agents. Its central tool is the
maximization of entropy, a variational principle. We review the history of this
principle, first considered as a law of nature, more recently as a procedure
for inference in model-making. And while equilibria (EQ) have long been
grounded in the principle of Maximum Entropy (MaxEnt), until recently no
equally foundational generative principle has been known for non-equilibria
(NEQ). We review evidence that the variational principle for NEQ is Maximum
Caliber. It entails maximizing \textit{path entropies}, not \textit{state
entropies}. We also describe the role of entropy in characterizing
irreversibility, and describe the relationship between MaxCal and other
prominent approaches to NEQ physics, including Stochastic Thermodynamics (ST),
Large Deviations Theory (LDT), Macroscopic Fluctuation Theory (MFT), and
non-extensive entropies.
