High temperature superconductivity is a major challenge of modern physics.  As a dramatic example of complex phenomena, a sophisticated understanding on the universality and diversity of these superconductors may lead to great revelations well beyond themselves.  While some physics of these oxides are already understood by their macroscopic and thermodynamic properties, but the truly deep insights often come from spectroscopy and scattering experiments.

As a hybrid of spectroscopy and scattering experiments, angle-resolved photoemission spectroscopy reveals the direction, the speed, and the scattering mechanism of valence electrons.  In the past two decades, enormously improved resolution and carefully matched experiments have elevated this technique from a band mapping tool to an important many-body spectroscopy.  Today, ARPES experiments help setting the intellectual agenda by testing new ideas, discovering surprises, and challenging orthodoxies.  This technique is at the focal point of the necessary debates leading to new paradigms of physics represented by the high temperature superconductors.

In this talk, we will survey the progress of this field over the last two decades and the information we gained about the high temperature superconductors: the dynamics of a single-hole in anti-ferromagnetic background, the evolution of the Mott gap, the anisotropic superconducting gap and the pseudogap, and the collective mode coupling. These findings have strongly influenced our thinking about these novel oxides.