  Quantum phase transitions of metals involve changes in the Fermi surface, and
can be divided into three categories. The first two categories involve symmetry
breaking, and lead to a deformation or reconstruction of the Fermi surface. The
third category involves a change in the volume enclosed by the Fermi surface
without any symmetry breaking: one phase is a Fermi liquid (FL) with the
conventional Luttinger volume, while the other phase is a `fractionalized Fermi
liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a
spin liquid with fractionalized excitations. It is a relatively simple matter
to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL
transition can also be present in single-band Hubbard-like models: this is
efficiently described by the `ancilla' method, which shows that the transition
is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is
argued to apply to the metallic states of the hole-doped cuprates. In the clean
limit, the critical properties of the quantum transitions in the three
categories are distinct, but all lead to perfect metal transport in the
quantum-critical regime. Impurity-induced `Harris disorder', with spatial
fluctuations in the local position of the quantum critical point, is a relevant
perturbation to the clean critical points. In the presence of Harris disorder,
all three categories exhibit strange metal behavior, which can be described by
a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.
