We discuss a new class of quantum phase transitions - deconfined Mott transition (DMT) - that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and an electrical insulator without Fermi surfaces of emergent neutral excitations. We construct a unified U(2) gauge theory to describe a variety of metallic and insulating phases, which include Fermi liquids, fractionalized Fermi liquids (FL∗), conventional insulators, and quantum spin liquids, as well as the quantum phase transitions between them. Using the DMT as a basic building block, we propose a distinct quantum phase transition - deconfined metal-metal transition (DM2T) - that describes a continuous transition between two metallic phases, accompanied by a jump in the size of their electronic Fermi surfaces (also dubbed a 'Fermi transition'). We study these new classes of deconfined metallic quantum critical points using a renormalization group framework at the leading nontrivial order in a controlled expansion and comment on the various interesting scenarios that can emerge going beyond this leading order calculation. We also study a U(1)×U(1) gauge theory that shares a number of similarities with the U(2) gauge theory and sheds important light on many phenomena related to DMT, DM2T, and quantum spin liquids. © 2020 authors. Published by the American Physical Society.