Quantum computation is a promising emerging technology which, compared to classical computation, allows for substantial speed-ups e.g. for integer factorization or database search. Despite several open issues concerning their physical realization, also how to efficiently design the corresponding quantum circuits remains an unsolved problem. While elaborated methods for design automation exists for conventional circuits and systems, respective solutions for quantum circuits are in its infancy. In particular, quantum mechanical phenomena such as superposition, phase shifts, or entanglement pose serious challenges to the development of proper design methods. The talk gives an overview on the current state of the art of the design automation for quantum circuits. Starting with an efficient representation of complex quantum functionality, important design tasks such as synthesis, verification, and simulation of quantum circuits are considered.