Sub-GeV dark matter particles produced via thermal freeze-out evade many of the strong constraints on heavier dark matter candidates. At the same time these particles face a multitude of new constraints from laboratory experiments, astrophysical observations and cosmological data. In my talk, I will review these constraints and the various ways how they can be satisfied. A particular focus is on models that systematically evade the very strong bounds on the annihilation rate of sub-GeV dark matter particles. I will present results from various global fits of these models, which not only determine the viable parameter regions, but also quantify the necessary fine tuning and allow for Bayesian model comparison. I will also discuss models that predict new signals that can be targeted with dedicated analyses in laboratory experiments and evaluate the discovery prospects of near-future experiments.