Computational techniques being developed for open quantum systems which allow for the simulation of the dynamical behaviour of realistic quantum technological systems on the nanoscale level, for example semiconductor defects and quantum dots. These computational methods should make possible the first principle calculations which are currently beyond the realm of standard approaches. In recent years Monte Carlo Wave Func- tion (Quantum Monte Carlo) techniques have been shown to provide an efficient numerical tool. In these techniques one propagates an ensemble of stochastic state vectors in the open system’s state space such that the reduced density matrix is recovered through an appropriate ensemble aver- age. These techniques have been well developed and have proven sufficient to describe Markovian systems and some strongly coupled non-Markovian systems. Specific projects in this area are presently aimed at simulating the dynamics of atoms in the double optical lattice and using Markovian techniques to simulate non-Markovian dynamics in open quantum systems.