Anyons are quantized excitations of correlated electron systems that obey statistics that are neither fermionic nor bosonic. I will describe recent advances in van der Waals heterostructures that now enable these types of particles to be probed in new ways. First, I will describe how recent technical imrovements have enabled us to measure key properties of the abelian anyons on the edge and in the bulk of a graphene-based fractional quantum Hall phase, including the determination of the topological quantization of tunneling exponent of the chiral Luttinger liquid and the interferometric measurement of the anyonic braiding phase at Landau level filling factor nu=1/3. Second, I will describe the recent surge of interest in fractional Chern insulators at zero magnetic field, and show how local magnetometry can be used to measure the thermodynamic gap of these phases.