The field of observational exoplanet science stands at the precipice of one of its founding objectives: the discovery and characterization of “Earth twin” planets orbiting nearby stars. The Doppler, or radial velocity (RV), method of exoplanet detection–which relies on measuring the gravitational reflex motion of a star orbited by planets–will be an essential part of discovering these planets, and evaluating their habitability. Within the past five years, new ultra-precise Doppler instrumentation has come online with sufficient measurement sensitivity to detect these “crown jewel” planets. However, recovering Earth twins requires mitigating the impacts of RV signals caused by variability on the surfaces of their host stars. Such astrophysical variability is present in all stars, at amplitudes orders of magnitude greater than those of the planets. In this presentation, I will introduce some of the new Doppler facilities that are pushing the boundaries of RV measurement precision beyond the longstanding 1 meter per second threshold. I will then describe new approaches to attacking the stellar variability problem, which leverage the unprecedented measurement precision afforded by these instruments to achieve sensitivity to exoplanets far beyond what was possible with last-generation spectrometers.