© 2020 authors. Published by the American Physical Society. Discrepant measurements of the Universe’s expansion rate (H0) may signal physics beyond the standard cosmological model. Here I describe two early modified gravity mechanisms that reconcile H0 value by increasing the expansion rate in the era of matter-radiation equality. These mechanisms, based on viable Horndeski theories, require significantly less fine-tuned initial conditions than early dark energy with oscillating scalar fields. In imperfect dark energy at equality (IDEE), the initial energy density dilutes slower than radiation but faster than matter, naturally peaking around the era of equality. The minimal IDEE model, a cubic Galileon, is too constrained by the cosmic microwave background (Planck) and baryon acoustic oscillations (BAO) to relieve the H0 tension. In enhanced early gravity (EEG), the scalar field value modulates the cosmological strength of gravity. The minimal EEG model, an exponentially coupled cubic Galileon, gives a Planck+BAO value H0=68.7±1.5 (68% CL), reducing the tension with SH0ES from 4.4σ to 2.6σ. Additionally, Galileon contributions to cosmic acceleration may reconcile H0 via late-universe phantom expansion (LUPE). Combining LUPE, EEG and Λ reduces the tension between Planck, BAO, and SH0ES to 2.5σ. I will also describe additional tests of coupled Galileons based on local gravity tests, primordial element abundances and gravitational waves. While further model building is required to fully resolve the H0 problem and satisfy all available observations, these examples show the wealth of possibilities to solve cosmological tensions beyond Einstein’s general relativity.