  We review the contributions of surface science methods to discover and
improve 3D topological insulator materials, while illustrating with examples
from our own work. In particular, we demonstrate that spin-polarized
angular-resolved photoelectron spectroscopy is instrumental to evidence the
spin-helical surface Dirac cone, to tune its Dirac point energy towards the
Fermi level, and to discover novel types of topological insulators such as dual
ones or switchable ones in phase change materials. Moreover, we introduce
procedures to spatially map potential fluctuations by scanning tunneling
spectroscopy and to identify topological edge states in weak topological
insulators.
