Deformed Heisenberg algebra with reflection appeared in the context of Wigner’s generalized quantization schemes underlying the concept of parafields and parastatistics of Green, Volkov, Greenberg and Messiah. We review the application of this algebra for the universal description of ordinary spin-jand anyon fields in2+1dimensions, and discuss the intimate relation between parastatistics and supersymmetry. ©2000 American Institute of Physics.