A plethora of qubit devices is under consideration for possible development ranging from quantum telereporters to quantum computers. The primary obstacle to the success of these efforts is the phenomenon of quantum decoherence, the rapid vanishing of the off-diagonal components of the reduced density matrix representing the computational degrees of freedom of the device. Following a review of the physics of quantum decoherence, several instructive examples are exposited. Decoherence issues associated with the various possible approaches to quantum computing are addressed. Also, possible generic methods are reviewed for surmounting the decoherence obstacle.