The etching of single crystal and polycrystalline Cu surfaces by halogens was studied using temperature programmed desorption (TPD), low energy electron diffraction (LEED), and scanning tunneling microscopy (STM). For Br2 and Cl2 on Cu(100) and polycrystalline Cu, the etching mechanism could be characterized as a two step process: 1) formation of a bulk Cu(I) halide, and 2) removal of the halide by sublimation. In all cases the first step was found to be adsorption rate limited. Halide formation was observed to consume Cu atoms from the step edge and thus etching can be considered the reverse of step flow growth. While STM showed that Cl2 reacts isotropically with steps on Cu(100), the rate of CuBr formation was observed to be sensitive to the local adsorbate structure at the step edge. For Cl2, it was found that halide removal could be characterized as a simple bulk sublimation process independent of the structure of the underlying Cu. In contrast, a CuBr desorption peak at temperatures lower than anticipated from bulk vapor pressure data was observed. The presence of narrowly spaced steps on the Cu surface was observed to stabilize this low-temperature desorption peak.