They have special cells called chromatophores.
Some species can rapidly change colour through mechanisms that translocate (relocate/move) pigment and reorient reflective plates within chromatophores.
Cephalopods such as the [octopus](https://en.wikipedia.org/wiki/Octopus) have complex chromatophore organs controlled by muscles/nerves to achieve this (which is very fast), whereas vertebrates such as [chameleons](https://en.wikipedia.org/wiki/Chameleon) generate a similar effect by [cell signalling](https://en.wikipedia.org/wiki/Cell_signaling). Such signals can be [hormones](https://en.wikipedia.org/wiki/Hormone) or [neurotransmitters](https://en.wikipedia.org/wiki/Neurotransmitter) (which is much slower) and may be initiated by changes in mood, temperature, stress or visible changes in the local environment
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