While it was originally believed that only bosons and fermions were allowed by quantum mechanics, in fact, when objects are restricted to move on a two-dimensional plane, new types of particles called "anyons" can emerge. For much of the last century it was believed that the only types of particles allowed by quantum mechanics are bosons (such as photons, phonons, pions, Higgs, etc.) and fermions (such as electrons, muons, quarks, etc.). This rule of only two particle types turns out to be a reflection of the dimensionality of space. When objects are restricted to move on a two-dimensional plane, new types of particles, called "anyons" can emerge. While originally just a theoretical fantasy, such particles have recently been observed in several different types of experiments. I will discuss the history of this field, why it is viewed as important, and recent progress. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/