The Hubble tension points to possible gaps in our understanding of physics around the epoch of recombination. A key aspect of the tension is its sensitivity to the sound horizon at decoupling, r_*, whose value depends on the microphysics of recombination. It is therefore highly desirable to obtain empirical constraints on both H_0 and r_* without relying on model-dependent assumptions. I will present recent work that demonstrates how combining baryon acoustic oscillations with CMB lensing enables such sound-horizon-agnostic measurements of the Hubble constant. I will also provide an update on primordial magnetic fields as a potential mechanism for alleviating the Hubble tension.