The recent BICEP2 measurement of B-mode polarization in the cosmic microwave background (r=0.2-0.05+0.07), a possible indication of primordial gravity waves, appears to be in tension with the upper limit from WMAP (r<0.13 at 95% C.L.) and Planck (r<0.11 at 95% C.L.). We carefully quantify the level of tension and show that it is very significant (around 0.1% unlikely) when the observed deficit of large-scale temperature power is taken into account. We show that measurements of TE and EE power spectra in the near future will discriminate between the hypotheses that this tension is either a statistical fluke or a sign of new physics. We also discuss extensions of the standard cosmological model that relieve the tension and some novel ways to constrain them.