In recent decades some cognitive scientists have adopted a program of quantum cognition. For example, Pothos and Busemeyer (PB) argue that there are empirical results concerning human decision-making and judgment that can be elegantly accounted for by quantum probability (QP) theory, while classical (Bayesian) probability theory fails. They suggest that the reason why QP works better is because some cognitive phenomena are analogous to quantum phenomena. This naturally gives rise to a further question about why they are analogous. Is this a pure coincidence, or is there a deeper reason? For example, could the neural processes underlying cognition involve subtle quantum effects, thus explaining why cognition obeys QP? PB are agnostic about this controversial issue, and thus their kind of program could be labeled as “weak quantum cognition” (analogously to the program of weak artificial intelligence as characterized by Searle). However, there is a long tradition of speculating about the role of subtle quantum effects in the neural correlates of cognition, constituting a program of “strong quantum cognition” (SQC) or “quantum cognitive neuroscience”. This paper considers the prospects of SQC, by briefly reviewing and commenting on some of the key proposals. In particular, Bohm and Hiley’s active information program will be discussed.