Highlights from the science case for an extremely large telescope are presented. As an introduction, theoretical performance gains in terms of FWHM and depth achievable with an ideal ELT working at the diffraction limit are compared with those for current 8m class telescopes. Three example science cases for an ELT are then presented, all of which drive the desired telescope size towards the largest currently being discussed, i.e. up to 100m. The science topics chosen from many are (1) direct detection of extra-solar planets, (2) study of resolved stellar populations in the Virgo cluster and (3) detection of the first luminous sources and re-ionization of the Universe. Finally, work that is currently taking place in Europe towards development of the science case for an ELT is described.