(color online) Schematic phase diagram of Ce-based narrow-band metals. At low density, the Ce 4f orbitals are singly occupied and carry a static moment (arrows), subject to long-range antiferromagnetic order (red line). Increasing the lattice density (e.g., by hydrostatic pressure) raises the hybridization between more extended orbitals (single-hatched region) and the 4f states, leading to dynamical frustration (Kondo spin-flips; double arrows), which in turn suppresses long-range order and induces an anomalous normal state. In the simplest case, at some distance from the quantum critical point at P_c1, where magnetic order is fully suppressed, this state can be modeled as a high-effective-carrier-mass Fermi liquid. Sufficiently close to P_c1, magnetically mediated pairing may induce unconventional superconductivity (red dome). Further increasing the hybridization between localized and extended orbitals leads eventually to a less correlated, metallic state (intermediate valence region), in which the 4f electrons delocalize through stronger hybridization with ligand states and occupy wider energy bands at the Fermi energy (cross-hatched region). The transition from the heavy fermion to the intermediate valence configuration may proceed through a first-order phase transition that involves a collapse of the unit cell volume with no change in lattice symmetry (green dashed line), driven by the gain in cohesive energy associated with the wide-band 4f electron configuration. If the critical endpoint of the first-order line is low enough, the system may become sufficiently soft at low temperatures to allow a superconducting state to form around the quantum phase transition associated with the volume collapse, at P_c2 (green dome). Reproduced with permission from Ref. [8].