One of the first nontrivial examples of quantum matter to be understood at equilibrium was the behavior of a chain of two-state spins, or qubits, entangled by nearest-neighbor interactions. Hans Bethe’s solution of the ground state in 1931 eventually led to the concept of Yang-Baxter integrability, and the thermodynamics were fully understood in the 1970s. However, the dynamical properties of this simple spin chain at any nonzero temperature remained perplexing until some unexpected theoretical and experimental progress beginning around 2019. Starting from this and other spin models appearing in Mott insulators, I will talk about how new atomic emulators and quantum computers are beginning to complement solid-state experiment and theory. The second part of the talk covers recent work on challenges such as finding spin liquids in Mott insulators, with a focus on new Yb-based compounds on the triangular lattice, and trying to understand possible instabilities of spin liquid phases.