I discuss quantum phase transitions associated with the onset of a broken space group or spin rotation symmetry in a two-dimensional metal. These can be divided into two broad classes, depending upon whether the order parameter is at zero or non-zero wavevector. In both cases it has been believed that a Gaussian theory due to Hertz provides an essentially complete description. I will argue that this is incorrect, and that a complete description requires strongly coupled field theories. I will discuss some general properties of such field theories.