In recent years, a number of observations have highlighted anomalies that might be explained by invoking dark matter annihilation. The excess of high energy positrons in cosmic rays reported by the PAMELA experiment is only one of the most prominent examples of such anomalies. Models where dark matter annihilates offer an attractive possibility to explain these
observations, provided that the annihilation rate is enhanced over the typical values given by conventional models of thermal relic dark matter annihilation. An elegant proposal to achieve this, is that of a Sommerfeld mechanism produced by a mutual interaction between the dark matter
particles prior to their annihilation. However, this enhancement can not be arbitrarily large without violating a number of astrophysical measurements. In this talk, I will discuss the degree to which these measurements can constrain Sommerfeld-enhanced models. In particular,
I will talk about constraints coming from the actual abundance of dark matter and the extragalactic background light measured at multiple wavelengths.