Determining the origin of structure in the universe is one of the most important open problems in cosmology. CMB anisotropies sourced by early-universe density perturbations are currently the most powerful observational probe of the earliest mechanisms of structure formation. It is possible that the same processes that produced the density perturbations also sourced tensor perturbations, or primordial gravitational waves (PGWs). If this is the case, detecting a PGW signal would yield insight into physics far earlier than the epoch of recombination, and allow us to build an unprecedented understanding of the earliest moments of time. PGWs leave imprints on the polarization of the CMB (Hu & White 1997; Kamionkowski et al. 1997; Seljak & Zaldarriaga 1997). In particular, the sensitivity of CMB measurements to gravitational waves arises from the generation of polarization at the surface of last scattering: to rst order, scalar perturbations produce only even-parity E-mode polarization, while tensor perturbations produce odd-parity B-mode polarization as well. Thus, a measurement of primordial B-mode polarization in the CMB, parameterized by the tensor-to-scalar ratio r, is a direct measurement of the amplitude of tensor perturbations. Detecting r has profound implications for high energy physics and the quantum nature of gravity (Krauss & Wilczek 2014), and the potential to shed light on the mechanism that produced these primordial perturbations. Cosmic in ation is our current leading paradigm for what occurred in the very early universe. It was rst put forward to explain the lack of observed magnetic monopoles and to solve the atness and horizon problems (Kazanas 1980; Starobinsky 1980; Sato 1981; Guth 1981; Linde 1982, 1983; Albrecht & Steinhardt 1982) and has since been an active eld of research. The theory describes a period of exponential expansion in which quantum uctuations are magnied to cosmic size and become the seeds for all structure in the universe (Mukhanov & Chibisov 1981, 1982; Guth & Pi 1982; Hawking 1982; Starobinsky 1982; Mukhanov 1985; Bardeen et al. 1986). In addition to the production of PGWs (for a recent review, see Kamionkowski & Kovetz 2016), in ation makes several predictions, most of which—superhorizon uctuations, Gaussian perturbations, adiabatic uctuations, spatial atness, and a nearly scale-invariant scalar spectral tilt—have been con rmed, most recently by the Planck collaboration (Planck Collaboration et al. 2020b).