The honeybee has one of the most complex social systems of any animal, and has been studied more than most invertebrates, but much is still unknown about its intelligence. The most controversial element is the "waggle dance." When returning to the hive after finding a source of food, honeybees perform an elaborate dance before collecting others to go retrieve the rest of the food. Dr. Karl von Frisch, working with Konrad Lorenz and Niko Tinbergen, won the Nobel Prize for Medicine in 1973 for their findings about the waggle dance. They suggest that the dance is an encoded message, telling other honeybees exactly where and how far away a source of food is, based on the angle of the dance, the speed of the waggle, and the time of day.
Another side, not mentioned by Boysen in The Smartest Animal on the Planet, insists that the dance merely attracts attention, and that an "odor plume" is the real communication--so the bees can just follow the scent of the food to its source.
But, honeybees are smarter than you'd think outside of their communication skills: they're possibly able to form cognitive maps (so they can recognize landmarks to find their way to a food source, even when placed somewhere they've never been) and can complete color discrimination tasks. One study placed a specific color at the entrance to a tunnel with a fork midway through. At the fork, one option has that same color, while the other option has a different color. The matching fork is the one with food at its end. Honeybees were very quickly able to figure out this pattern, even when presented with new colors. By lengthening the tunnel before the fork, researchers showed their short-term memory is roughly five seconds--about the same as that of birds.