The simplest theory of electrons in a metal ignores their Coulomb repulsion, and has the electrons occupy plane wave states inside a Fermi surface in momentum space. Remarkably, the Fermi surface survives even with Coulomb interactions—it can change its shape, but the Luttinger theorem states that the enclosed volume must be preserved. Modern theories of entangled electrons show that it is possible to evade the Luttinger theorem and obtain smaller Fermi surfaces, provided fractionalized excitations and emergent gauge fields are present. I will connect these ideas to recent observations in the heavy fermion and cuprate materials.