An electron injected into liquid helium forces open a small cavity that is free of helium atoms. This object is referred to as an electron bubble, and has been studied experimentally and theoretically for many years. At first sight, it would appear that because helium atoms have such a simple electronic structure and are so chemically inert, it should be very easy to understand the properties of these electron bubbles. However, it turns out that while for some properties theory and experiment are in excellent quantitative agreement, there are other experiments for which there is currently no understanding at all.