Morphologically complex flowers are characterized by bilateral symmetry, tube-like shapes, deep corolla tubes, fused petals, and/or poricidal anthers, all of which constrain the access of insect visitors to floral nectar and pollen rewards. Only a subset of potential pollinators, mainly large bees, learn to successfully forage on such flowers. Thus, complexity may comprise a morphological filter that restricts the range of visitors and thereby increases food intake for successful foragers. Such pollinator specialization, in turn, promotes flower constancy and reduces cross-species pollen transfer, providing fitness benefits to plants with complex flowers. Since visual signals associated with floral morphological complexity are generally honest (i.e., indicate food rewards), pollinators need to perceive and process them. Physiological studies show that bees detect distant flowers through long-wavelength sensitive photoreceptors. Bees effectively perceive complex shapes and learn the positions of contours based on their spatial frequencies. Complex flowers require long handling times by naive visitors, and become highly profitable only for experienced foragers. To explore possible pathways towards the evolution of floral complexity, we discuss cognitive mechanisms that potentially allow insects to persist on complex flowers despite low initial foraging gains, suggest experiments to test these mechanisms, and speculate on their adaptive value.