Searching for evidence of inflation by measuring B-modes in the cosmic microwave background (CMB) polarization at degree angular scales remains one of the most compelling experimental challenges in cosmology. BICEP2 and the Keck Array are part of a program of experiments at the South Pole whose main goal is to achieve the sensitivity and systematic control necessary for measurements of the tensor-to-scalar ratio at σ(r) ~0:01. Beam imperfections that are not sufficiently accounted for are a potential source of spurious polarization that could interfere with that goal. The strategy of BICEP2 and the Keck Array is to completely characterize their telescopes' polarized beam response with a combination of in-lab, pre-deployment, and on-site calibrations. We Sereport the status of these experiments, focusing on continued improved understanding of their beams. Far-field measurements of the BICEP2 beam with a chopped thermal source, combined with analysis improvements, show that the level of residual beam-induced systematic errors is acceptable for the goal of σ(r) ~ 0:01 measurements. Beam measurements of the Keck Array side lobes helped identify a way to reduce optical loading with interior cold baffles, which we installed in late 2013. These baffles reduced total optical loading, leading to a ~ 10% increase in mapping speed for the 2014 observing season. The sensitivity of the Keck Array continues to improve: for the 2013 season it was 9:5 μK _/s noise equivalent temperature (NET). In 2014 we converted two of the 150-GHz cameras to 100 GHz for foreground separation capability. We have shown that the BICEP2 and the Keck Array telescope technology is sufficient for the goal of σ(r) ~ 0:01 measurements. Furthermore, the program is continuing with BICEP3, a 100-GHz telescope with 2560 detectors.