**Quantum phase transitions in 2d metals: non-Fermi-liquid behavior and superconductivity**

A central question of modern condensed matter physics is how can our standard description of metals, the Landau Fermi-liquid theory, breakdown. In this light, quantum phase transitions associated with onset of order in metals have attracted much interest. Strong order parameter fluctuations present at the quantum critical point (QCP)
tend to destroy the Landau quasiparticles, leading to non-Fermi-liquid
behavior. In addition, the same order parameter fluctuations provide
the glue for Cooper pair formation. Hence, an important question is
whether a QCP in a metal is inherently unstable to superconductivity.
In this talk, I will demonstrate that the answer to this question is
"yes" using as prototypical examples transitions involving the onset
of i) Ising-nematic order, ii) spin-density-wave order. For the case
of the Ising-nematic transition, I will present fully controlled
renormalization group calculations proving the superconducting
instability. For the spin-density-wave transition, relevant to
cuprate, pnictide and heavy-fermion materials, I will combine
analytical arguments with unbiased, sign-problem free quantum
Monte-Carlo simulations to establish the emergence of an
unconventional superconductor near the transition.