The electron system with its many phases and realizations remains a fascinating subject of study. It has been extensively analysed in three, two, one and zero dimensions, as well as in confined nanoscopic and mesoscopic geometries generated with microfabrication techniques. An obvious next step in this investigation is to study the electron system in curved geometries. In particular we will focus in these lectures on the two‐dimensional spherical electron system, realized in for example multielectron bubbles (MEBs), buckyballs, and nanoshells. © 2003 American Institute of Physics