Real-time simulations on the lattice: quantum, classical and in-between

I give a brief introduction to the use of lattice field methods for studying quantum evolution (way) out of equilibrium. I emphasize the way in which the numerically simple, and very successful, classical-statistical approximation is related to the much more involved quantum evolution and the 2PI-formalism which in a sense is in-between. I give some illustrative examples of seminal and recent applications of these methods. This is not meant as a comprehensive and balanced review of the state-of-the art of the field, but as a primer and overview for lattice field theory scientists interested in making an excursion from 4-D Euclidean space to 3+1 Minkowski signature.