Squat lobsters are lobster-like crustaceans with flat bodies and short tails (usually kept curled under their bodies), giving them a short, 'squat' appearance. It was originally assumed that all squat lobsters were related, and they were placed in the superfamily Galatheoidea, but with the advent of DNA sequencing it was determined that this is not the case.
Currently, squat lobsters are split between the superfamily Galatheoidea (which also contains the porcelain crabs) and the superfamily Chirostyloidea (which also includes the yeti crab); with over 900 recognized species and 60 genera, 'squat lobsters' is a wide ranging group.
Generally, squat lobsters look like small, tailless lobsters. In some cases their tails look quite a bit like lobster tails, and are simply curled down under their body; in other cases the curled tails are really very short, and don't look much longer uncurled. As you might expect, there is a fair amount of variation, and while most squat lobsters look pretty much the same, there are impressive species out there; the Lauriea siagiani, or Hairy Squat Lobster looks quite a lot like the yeti crab to which is it related... except purple.
Squat lobsters often have long front arms with elongated claws, and can be found perched on corals with arms and claws wide open, waiting for something edible to drift by. They may take a sharp eye to spot; they range from about 18 millimeters to 90 millimeters (0.70 inches to 3.5 inches) in length, although this is body length, and does not count the arms, which may often be as long as the body.
Squat lobsters live pretty much everywhere, from hydrothermal vents to coral reefs, with at least one species that lives above sea level in coastal lava tubes. Most spend most of their lives on the seafloor, or climbing on sessile creatures, but some species swim in swarms in the water column hunting plankton. Some are predators, some are scavengers, and some are filter feeders; there is even one species that lives entirely on wood that has been swept into the ocean (including shipwrecks).
Speaking of eating, humans do sometimes eat squat lobsters, in which case they will most often be called simply langostino (in English; in other languages this means other things), or sometimes, lobster. Seafood chain Long John Silver's got in some trouble in 2006 when it marketed squat lobster as "lobster bites", and there have been other cases of processed "lobster" meat actually being langostino.