Although originally classified as galaxies, Ultra-Compact Dwarfs (UCDs) have many properties in common with globular star clusters. The debate on the origin and nature of UCDs, and the recently discovered ultra-faint dwarf spheroidal (dSph) galaxies which contain very few stars, has motivated us to as the question ‘What is a galaxy?’ Our aim here is to promote further discussion of how to define a galaxy and, in particular, what separates it from a star cluster. Like most previous definitions, we adopt the requirement of gravitationally bound stellar system as a minimum. In order to distinguish a dwarf galaxy from a globular cluster, we discuss other possible requirements, such as a minimum size, a long two-body relaxation time a satellite system, the presence of complex stellar populations and non-baryonic dark matter. We briefly mention the implications of the adoption of each of these definitions. Some special cases of objects with a ambiguous nature are also discussed. Finally, we give our favoured criteria, and in the spirit of ‘collective wisdom’, invite readers to vote on their prefered definition of a galaxy via a dedicated website.