In recent years a lot of interest has been raised by quantum phase transitions involving a smooth disappearance of a Fermi-surface. As one approaches such critical points, the Landau-quasiparticle weight and velocity tend to zero, nevertheless, the Fermi surface remains sharply defined. One proposed example of such a transition is the development of Ising-nematic order in a metal. This order, associated with electronic correlations, which spontaneously break the square lattice symmetry to that of a rectangular lattice, has been observed in the enigmatic normal state of the cuprate superconductors by a number of recent experiments. Motivated by these findings, I will present the scaling theory of the Ising-nematic transition in a two-dimensional metal. The critical point is described by an infinite set of 2+1 dimensional local field theories, labeled by points on the Fermi surface. Scaling forms for the response functions are proposed, and supported by computations up to three loops. Our results extend also to the theory of a Fermi surface coupled to a U(1) gauge field, which describes a number of spin and charge-liquid states.