In solid-state physics two different paradigms are typically applied. The first is a local picture, in which one visualizes the quantum states of electrons in atomic orbitals or at impurity atoms in real space (r-space). The second is the momentum or reciprocal space (k-space) picture, where electrons are viewed as de Broglie waves completely delocalized throughout the material. Understanding these two separate paradigms is essential for a complete understanding of the physics of condensed matter, but rarely has it been as necessary to combine both pictures as it has been to gain insight into the electronic structure of the high-temperature superconductors (HTSCs). In this article, we review recent developments in the understanding of the relationship between the r-space and k-space electronic spectroscopies used to explore high-temperature superconductivity. © 2008 Elsevier Ltd. All rights reserved.