The attempt to employ quantum principles for modeling cognition has enabled the introduction of several new concepts in psychology, such as the uncertainty principle, incompatibility, entanglement, and superposition. For many commentators, this is an exciting opportunity to question existing formal frameworks (notably classical probability theory) and explore what is to be gained by employing these novel conceptual tools. This is not to say that major empirical challenges are not there. For example, can we definitely prove the necessity for quantum, as opposed to classical, models? Can the distinction between compatibility and incompatibility inform our understanding of differences between human and nonhuman cognition? Are quantum models less constrained than classical ones? Does incompatibility arise as a limitation, to avoid the requirements from the principle of unicity, or is it an inherent (or essential?) characteristic of intelligent thought? For everyday judgments, do quantum principles allow more accurate prediction than classical ones? Some questions can be confidently addressed within existing quantum models. A definitive resolution of others will have to anticipate further work. What is clear is that the consideration of quantum cognitive models has enabled a new focus on a range of debates about fundamental aspects of cognition.