The honeybee Apis mellifera, with a brain of only 960,000 neurons and the ability to perform sophisticated cognitive tasks, has become an excellent model in life sciences and in particular in cognitive neurosciences. It has been used in our laboratories to investigate brain and behavioural asymmetries, i.e., the different functional specializations of the right and the left sides of the brain. It is well known that bees can learn to associate an odour stimulus with a sugar reward, as demonstrated by extension of the proboscis when presented with the trained odour in the so-called Proboscis Extension Reflex (PER) paradigm. Bees recall this association better when trained using their right antenna than they do when using their left antenna. They also retrieve short-term memory of this task better when using the right antenna. On the other hand, when tested for long-term memory recall, bees respond better when using their left antenna. Here we review a series of behavioural studies investigating bees' lateralization, integrated with electrophysiological measurements to study asymmetries of olfactory sensitivity, and discuss the possible evolutionary origins of these asymmetries. We also present morphological data obtained by scanning electron microscopy and two-photon microscopy. Finally, a behavioural study conducted in a social context is summarised, showing that honeybees control context-appropriate social interactions using their right antenna, rather than the left, thus suggesting that lateral biases in behaviour might be associated with requirements of social life