  Tunneling spectroscopy played a central role in the experimental verification
of the microscopic theory of superconductivity in the classical
superconductors. Initial attempts to apply the same approach to
high-temperature superconductors were hampered by various problems related to
the complexity of these materials. The use of scanning tunneling
microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the
main difficulties. This success motivated a rapidly growing scientific
community to apply this technique to high-temperature superconductors. This
paper reviews the experimental highlights obtained over the last decade. We
first recall the crucial efforts to gain control over the technique and to
obtain reproducible results. We then discuss how the STM/STS technique has
contributed to the study of some of the most unusual and remarkable properties
of high-temperature superconductors: the unusual large gap values and the
absence of scaling with the critical temperature; the pseudogap and its
relation to superconductivity; the unprecedented small size of the vortex cores
and its influence on vortex matter; the unexpected electronic properties of the
vortex cores; the combination of atomic resolution and spectroscopy leading to
the observation of periodic local density of states modulations in the
superconducting and pseudogap states, and in the vortex cores.
