All fundamental particles obey bosonic or fermion statistics, but for effective theories in low dimensional systems, topological quantization provides a non standard possibility: anyons. Anyons in two-dimensional systems are theoretically well-understood and quasiparticles with anyons obeying fractional statistics have been directly measured. A proliferation of theoretical models has sought to replicate anyons with fractional statistics in one-dimensional systems, and recent experimental advances with ultracold atoms in one-dimensional optical traps have implemented some of these models. What can we learn about indistinguishability, topological interactions, and topological quantum computation from these models? And wait … are anyons even possible in one dimension? In this talk, I will motivate the search for anyons in one dimension, explain the three interaction mechanisms that generate one-dimensional anyons, and comment on recent experimental implementations.