Artin fans are logarithmic algebraic stacks that are logarithmically étale over an algebraically closed base field. Despite their seemingly abstract definition, the geometry of Artin fans can be described completely in terms of combinatorial objects, so called cone stacks, i.e. geometric stacks over the category of rational polyhedral cones. In this talk, I am going to give an expository account of the theory of Artin fans, focusing on the connection with cone stacks. Given time I will also discuss work-in-progress with R. Cavalieri, M. Chan, and J. Wise, on how cone stacks form a natural framework in order to study the moduli stack of tropical curves.