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The Lyα emission line has been proven to be a powerful tool for studying evolving galaxies at the highest redshift. However, in order to use Lyα as a physical probe of galaxies, it becomes vital to know the Lyα escape fraction (f^(Lyα)_(esc)). Unfortunately, due to the resonant nature of Lyα, f^(Lyα)_(esc) may vary unpredictably and requires empirical measurement. Here, we compile Lyα luminosity functions (LFs) between redshifts z = 0 and 8 and, combined with Hα and ultraviolet data, assess how f^(Lyα)_(esc) evolves with redshift. We find a strong upward evolution in f^(Lyα)_(esc) over the range z = 0.3-6, which is well fit by the power law f^(Lyα)_(esc)α(1 + z)^ξwith ξ = (2.57^(+0.19)_(–0.12)). This predicts that f^(Lyα)_(esc) should reach unity at z = 11.1. By comparing f^(Lyα)_(esc) and E_(B–V) in individual galaxies we derive an empirical relationship between f^(Lyα)_(esc) and E_(B–V) , which includes resonance scattering and can explain the redshift evolution of f^(Lyα)_(esc) between z = 0 and 6 purely as a function of the evolution in the dust content of galaxies. Beyond z ≈ 6.5, f^(Lyα)_(esc) drops more substantially, an effect attributed to either ionizing photon leakage, or an increase in the neutral gas fraction of the intergalactic medium. While distinguishing between these two scenarios may be extremely challenging, by framing the problem this way we remove the uncertainty of the halo mass from Lyα-based tests of reionization. We finally derive a new method by which to estimate the dust content of galaxies, based purely upon the observed Lyα and UV LFs. These data are characterized by an exponential with an e-folding scale of z_(EBV) ≈ 3.4.