Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schroedinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC codes. Various examples are shown of our theoretical results compared with those obtained from Synchrotron Radiation facilities and from Satellite observations. We also indicate future directions and implementation of the R-matrix codes on emerging GPU architectures.