Glass microsphere resonators that support optical resonances known as whispering-gallery modes are unique tools for studying and exploiting optical effects under extremely well controlled conditions. In this paper, a review focusing mostly on glass microsphere resonators is presented. First, a brief historical background is given in which we see how the state-of-the-art has grown from novel optical resonators to the ultrahigh Q cavities used in cutting-edge experiments. After the basic properties of microsphere resonators are outlined we will discuss some of the recent experiments involving microsphere resonators, although some discussion involving polymeric microspheres is also included. The use of doped and undoped microspheres in optical signal processing, optical sensing and quantum optics is highlighted. Finally, there is a brief review of recent optomechanical experiments that use microspheres.