  Quantum theories constructed on the noncommutative spacetime called the
Groenewold-Moyal(GM) plane exhibit many interesting properties such as
causality violation, Lorentz and CPT non-invariance and twisted statistics.
Such violations lead to many striking features that may be tested
experimentally. Thus these theories predict Pauli-forbidden transitions due to
twisted statistics, anisotropies and acausal effects in the cosmic microwave
background radiation in correlations of observables and Lorentz and CPT
violations in scattering amplitudes. Such features of quantum physics on the GM
plane are surveyed in this review.
