We may often take it for granted that human vision is limited to what we call the 'visible light' spectrum. Human vision is based on small-molecule photopigments or 'chromophores' that absorb photons and change their shape by photoisomerization, coupled with a protein that transduces the signal for downstream use. However, other organisms can sense light outside the range visible to us. Why can't we see infrared and ultraviolet?
Rather famously, bees have co-evolved with flowering plants to use ultraviolet wavelengths for flowers to display, and bees to sense, where pollen and nectar may be found. Human photoreceptors are also sensitive to UV light, although our corneas filter out this damaging source of radiation to protect our delicate retinas. The benefit for bees and other insects may outweigh the need to filter UV light because of their relatively short lifespans (only a few weeks for workers, compared with ~80 years for humans).
Pit vipers, bats, and other nocturnal hunters can sense infrared light emitted by their warm-blooded prey, using heat-sensitive ion channels instead of the chromophore/protein system that we use, as well as pinhole-camera-like 'pits' and/or folds on their snouts rather than a lens to generate a spatial image across a sensor array.
A recent paper (Luo et al., Science 332, 2011) showed that heat and light based effects in chromophores become confused at longer wavelengths, severely limiting signal-to-noise ratios (SNRs), limiting their use for IR sensing. Short wavelengths like UV are absorbed non-specifically by the proteins that transduce what the chromophores sense, and so noise (and damage) may ensue in the sensing pathway. Flowers may use high contrast displays to make SNR less relevant for bees. Bees also appear to use UV polarization to identify targets for navigation, which may explain in part why they take such wandering flight paths toward their targets, which may in turn help them to gather parallax or 'stereo' information about UV polarization.
Another recent result (Christie et al., Science 335, 2012) reveals a novel mechanism for sensing UV light in plants, using protein-protein interactions without a small-molecule chromophore in the mix. Plants use this information to create 'sunblock'-like effects in their tissues. Plants may be able to use this information much more slowly for their purposes than humans or bees, which may explain the difference in the mechanisms used.