Figure 1: (Top) Schematic phase diagram of cuprate superconductors as function of temperature $T$ and doping level $p$. At half-filling, $p=0$, the materials are antiferromagnetic (AF) Mott insulators; superconductivity (SC) thus emerges from doping a Mott insulator. The doping range $p<0.16$ ($p>0.16$) is dubbed underdoped (overdoped), and the underdoped regime, $p<0.16$, is characterized by the pseudogap. Quantum oscillations have been detected at low $T$ in large applied fields. (Bottom) Schematic evolution of the Fermi surface in a density-wave scenario. All panels show a quarter of the two-dimensional Brillouin zone, with occupied states shaded. On the far overdoped side, a large unreconstructed Fermi surface is seen. For smaller doping, but $p>p_c$, the density-wave reconstruction induces electron pockets near $(0,\pi )$, whereas those disappear for $p<p_c$ in favor of open orbits. (The existence of smaller pockets depends on microscopic details.)