Many species of octopuses (and some other cephalopods) have extremely efficient mechanisms for camouflaging themselves against coloured backgrounds. They also use coloured patterns for communication and for repelling predators. The physical mechanisms for generating the colours in their skin is well understood (see Chromatophore at Wikipedia).

Microscopic examinations of the octopus eye, however, have shown that they don't have the necessary retinal cells (photoreceptors) to perceive colour. Also, laboratory experiments which have attempted to test their vision skills have found, in all cases, that they appear to be profoundly colour-blind.

Raising the question of how they can camouflage themselves to precisely match a background - the colours of which they can't see. The system also appears to work in extremely low light conditions.

The extreme range of coloured displays which they are known to use to communicate with each other is also unexplained, given that the recipient apparently can't see the colours.

A theory presented in PNAS vol. 113 no. 29, 2016, suggests that they might be using chromatic aberration (i.e. colour separation caused by diffraction) due to their unusual slot-like pupil shape. Source

Other theories suggest that the octopus skin itself may somehow be able to perceive colours - but the photoreceptors which have been found in the skin also appear to be monochromatic.

- the photoreceptors found in an octopus’s skin are, like those in its eyes, insufficient to detect colour. The best working hypothesis is that some complex interaction between the skin’s photoreceptors and chromatophores allows the octopus to adopt colours it cannot see."

Amia Srinivasan,London Review of Books , Vol. 39 No. 17, September 2017.

Further reading (with photos) : Cephalopod dynamic camouflage in Current Biology, Volume 17, Issue 11.

Update Aug. 2023

A study published in nature communications describes work on the skin of the hogfish (Lachnolaimus maximus). The research group found that the skin of the fish is capable of 'dermal photoreception' - meaning that the skin can locally 'see' colours using 'phototransduction proteins' called 'opsins'. They go on to suggest that this capability may be able to explain rapid colour changes in some fish without the need for colour input via the eyes. If confirmed, it's possible that a similar mechanism may be at work in cephalopods like the octopus.

Though these studies evidence a relationship between dermal opsins and dynamic color change we still lack knowledge about the functional organization of this system—perhaps critical for understanding the significance of dermal photoreception in living animals.

Source : Dynamic light filtering over dermal opsin as a sensory feedback system in fish color change