We attempt to restore an integrative perspective on what the scientific problems of the cognitive sciences are and how they arise. As a point of departure, we draw attention to an increasingly impoverished view of science as empirical problem-solving. This frame, while occasionally useful, is typically fraught with misconceptions. We explicate some of its undesirable consequences, such as the neglect of plausibility constraints on cognitive explanations. Briefly, we challenge the implied autonomy of so-called empirical problems, the overemphasis on solving them versus finding them, and an overly narrow construal of what it means to solve them. To lift this epistemic fog, we bring theoretical problem-finding out of obscurity as a core activity in the cognitive scientist's toolbox. We illustrate various issues through hypothetical and factual case studies; among them, the inadequacies of portraying empirical problems as separate from theoretical problems; how phenomena in need of explanation depend critically on theoretical problems and plausibility constraints; and how theoretical problem-finding can be productive even when no immediate solutions are possible. Along the way, we give concrete examples of what can go wrong if we neglect the role of theoretical problems in shaping scientific questions. We arrive at an integrative account of how phenomena of interest, and cognitive-scientific problems more broadly, are carved out through theoretical problem-finding.