Sachdev developed the theory of quantum transport at non-zero temperatures in the simplest model system without quasiparticle excitations: a conformal field theory in 2+1 dimensions, realized by the superfluid-insulator transitions of ultracold bosons in an optical lattice. A comprehensive picture emerged from quantum-Boltzmann equations, the operator product expansion, and holographic methods. The latter mapped the dynamics to that in the vicinity of the horizon of a black hole. These were the first proposed connections between condensed matter quantum critical systems, hydrodynamics, and quantum gravity. These works eventually led to the theory of hydrodynamic transport in graphene, and the successful experimental predictions described below. Quantum matter without quasiparticles Sachdev developed the theory of magneto-thermoelectric transport in 'strange' metals: these are states of quantum matter with variable density without quasiparticle excitations. Such metals are found, most famously, near optimal doping in the hole-doped cuprates, but also appear in numerous other correlated electron compounds. For strange metals in which momentum is approximately conserved, a set of hydrodynamic equations were proposed in 2007, describing two-component transport with momentum drag component and a quantum-critical conductivity. This formulation was connected to the holography of charged black holes, memory functions, and new field-theoretic approaches. These equations are valid when the electron-electron scattering time is much shorter than the electron-impurity scattering time, and they lead to specific predictions for the density, disorder, temperature, frequency, and magnetic field dependence of transport properties. Strange metal behavior obeying these hydrodynamic equations was predicted in graphene, in the 'quantum critical' regime of weak disorder and moderate temperatures near the Dirac density. The theory quantitatively describes measurements of thermal and electrical transport in graphene, and points to a regime of viscous, rather than Ohmic, electron flow. Extensions of this theory to Weyl metals pointed out the relevance of the axial-gravitational anomaly, and made predictions for thermal transport which were confirmed in observations (and highlighted in the New York Times). Phases of the high temperature superconductors High temperature superconductivity appears upon changing the electron density away from a two-dimensional antiferromagnet. Much attention has focused on the intermediate regime between the antiferromagnet and the optimal superconductor, where additional competing orders are found at low temperatures, and a "pseudogap" metal appears in the hole-doped cuprates. Sachdev's theories for the evolution of the competing order with magnetic field, density, and temperature have been successfully compared with experiments. Sachdev and collaborators proposed a sign-problem free Monte Carlo method