Anyons are strikingly unique particles in (usually) two-dimensional quantum condensed matter, where their physical properties such as charge, spin and mass may become fractions of that of whole particles. The exchange of two such particles (see Figure 1), in stark contrast to the strictly fermionic and bosonic statistics in three-dimensions, leads to anyonic statistics, where the exchange phase can take nearly arbitrary value. In more exotic non-Abelian anyons, this exchange operation may even be represented by a unitary matrix. The depth of unexplored fundamental physics in ‘anyonic matter’ and potential applications in robust quantum information infrastructure makes the search for an accessible anyonic platform a challenging but exciting field at the forefront of condensed matter physics.