In this talk I will discuss the notion of computational zero-knowledge in the quantum setting, and the related notion of quantum computational indistinguishability. An investigation of these notions reveals some interesting properties that are unique to quantum information, and suggest that particularly strict notions of security of quantum cryptographic primitives may be required in common settings. For example, a strong definition of indistinguishability for computationally concealing commitment schemes is (evidently) required for known quantum zero-knowledge proofs for NP.