To cope with the complexity of simulating quantum computations, several approaches are currently investigated---ranging from straight-forward realizations of the corresponding matrix-vector multiplications through arrays to dedicated HPC-solutions exploiting massive hardware power. In this talk, an alternative is presented utilizes decision diagrams. These provide a compact representation of quantum states and operations for many (practically-relevant) instances and allow for an efficient simulation. The talk will review the underlying ideas of decision diagrams and how to put them into use for corresponding simulation schemes. This will be followed by a discussion on the performance of the resulting solutions (featuring both, the strength but also the weaknesses of decision diagram-based simulation) as well as a brief overview of corresponding open-source implementations.