It is a familiar experience to perceive a material object as maintaining a stable shape even though it projects differently shaped images on our retina as we move with respect to it, or as maintaining a stable color throughout changes in the way the object is illuminated. We also perceive sounds as maintaining constant timbre and loudness when the context and the spatial relations between us and the sound source change over time. But where does this perceptual invariance ‘come from’? What is it about our perceptual systems that makes them able to ‘transform’ incoming unstable and fluctuating sensory inputs into generally stable and coherent conscious experiences? And what exactly do we experience as invariant in cases like those described above? There are two main approaches to the Problem of Perceptual Invariance: the Local-Inferential approach and the Global-Structural approach. Although both approaches include an account of the sub-personal perceptual mechanisms ‘stabilizing’ variant and invariant components in incoming sensory stimulation and a proposal regarding the phenomenology of perceptual invariance, in this paper I argue that the latter provides a better solution to the problem overall.