  Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed
by rock. This simple game is popular among children and adults to decide on
trivial disputes that have no obvious winner, but cyclic dominance is also at
the heart of predator-prey interactions, the mating strategy of side-blotched
lizards, the overgrowth of marine sessile organisms, and the competition in
microbial populations. Cyclical interactions also emerge spontaneously in
evolutionary games entailing volunteering, reward, punishment, and in fact are
common when the competing strategies are three or more regardless of the
particularities of the game. Here we review recent advances on the
rock-paper-scissors and related evolutionary games, focusing in particular on
pattern formation, the impact of mobility, and the spontaneous emergence of
cyclic dominance. We also review mean-field and zero-dimensional
rock-paper-scissors models and the application of the complex Ginzburg-Landau
equation, and we highlight the importance and usefulness of statistical physics
for the successful study of large-scale ecological systems. Directions for
future research, related for example to dynamical effects of coevolutionary
rules and invasion reversals due to multi-point interactions, are outlined as
well.
