While the view that we perceive aesthetic properties may seem intuitive, it has received little in the way of explicit defence. It also gives rise to a puzzle. The first strand of this puzzle is that we often cannot perceive aesthetic properties of artworks without training, yet much aesthetic training involves the acquisition of knowledge, such as when an artwork was made, and by whom. How, if at all, can this knowledge affect our perception of an artwork’s aesthetic properties? The second strand of the puzzle arises when we widen the scope of aesthetic experience. The very same aesthetic properties that seem to require training for their perception in artworks do not appear to require training to perceive in objects of everyday aesthetic appreciation and natural phenomena. In this paper I argue that a prominent extant attempt to explain how training is compatible with aesthetic perception—cognitive permeation—is an inadequate solution. I also develop a positive view of aesthetic perception that provides a unified solution to both strands of the puzzle.