An electron injected into liquid helium forces open a small cavity of diameter 4 nm referred to as an "electron bubble". In this talk I will describe experiments in which we study the properties of these unique nanostructures. We have used an ultrasonic technique to make movies showing the motion of individual electrons. In other experiments, we have discovered that some electron bubbles are smaller than the normal electron bubble. We will discuss the ideas that have been put forward to explain the possible structure of these objects.