The Phallaceae or stinkhorns, are a family of basidiomycetes which produce a foul-scented, phallus-shaped mushroom. They belong to the order Phallales. Their method of reproduction is different than most mushrooms, which use the air to spread their spores. Stinkhorns instead produce a sticky spore mass on their tip which has an odor of carrion, dung, or other things that attract flies. The flies land on the stinkhorn and in doing so collect the spore mass on their legs and carry it to other locations.
These fungi are theoretically edible in their immature "egg" state, but few people have the urge to consume such small, foul-smelling mushrooms. However, after frying in oil they have a fishy taste.
Stinkhorns develop from round structures called 'eggs', which do not have the odour of mature specimens. They can be seen in the photograph of Mutinus elegans and also in the following photo which shows one cut in half. You can see the whole mature fruiting body compressed into the 'egg' and ready to expand into its adult state.
The Clathrus columnatus, the orange and red variant of stinkhorn with the "arms" coming together at the top, is also known as an octopus stinkhorn, deadman's fingers, and Devil's nose.