256 The original definition of a topological insulator was as a time-reversal-symmetric insulator in which spin-orbit coupling leads to protected metallic edge or surface states. An alternate definition comes from considering the effect of a small perturbation that breaks the symmetry and gaps the surfaces; then the material can be viewed as having a quantized magnetoelectric effect. We discuss generalizations of this result to other materials and symmetry classes. In closing we discuss how a version of BF theory can capture both definitions of a topological insulator in either 2D or 3D, just as the Chern-Simons effective theory captures the universal features of quantum Hall states. Possible generalizations to "fractional" topological insulators are discussed. Tage Erlander Award Conference "Frontiers of Condensed Matter Physics" Joel Moore (Berkeley) None