I will talk about quaternionic analysis over the Heisenberg groups: the tangential $k$-Cauchy-Fueter complexes, Hartogs' phenomenon for $k$-CF functions over the (right quaternionic) Heisenberg group, and quaternionic pluripotential theory over the Heisenberg group, including plurisubharmonic functions, the quaternionic Monge-Ampere operator and closed positive currents etc.