The Lyman alpha emission line (Lyα) of neutral hydrogen (Hi) is intrinsically the brightest emission feature in the spectrum of astrophysical nebulae, making it a very attractive observational feature with which to survey galaxies. Moreover as an ultraviolet resonance line, Lyα possesses several unique characteristics that make it useful to study the properties of the interstellar medium and ionising stellar population at all cosmic epochs. In this review, I present a summary of Lyα observations of galaxies in the nearby universe. By ultraviolet continuum selection, at the magnitudes reachable with current facilities, only ≈ 5% of the local galaxy population shows a Lyα equivalent width (WLyα) that exceeds 20 Å. This fraction increases dramatically at higher redshifts, but only in the local universe can we study galaxies in detail and assemble unprecedented multi-wavelength datasets. I discuss many local Lyα observations, showing that when galaxies show net Lyα emission, they ubiquitously also produce large-scale halos of scattered Lyα, that dominate the integrated luminosity. Concerning global measurements, we discuss how WLyα and the Lyα escape fraction (fLyαesc) are higher (WLyα ≳ 20 Å and fLyαesc ≳ 10%) in galaxies that represent the less massive and younger end of the distribution for local objects. This is connected with various properties, such that Lyα-emitting galaxies have lower metal abundances (median value of 12 + log(O/H) ~ 8.1) and dust reddening. However, the presence of galactic outflows/winds is also vital to Doppler shift the Lyα line out of resonance with the atomic gas, and high WLyα is found only among galaxies with winds faster than ~ 50 km s−1. The empirical evidence is then assembled into a coherent picture, and the requirement for star-formation-driven feedback is discussed in the context of an evolutionary sequence where the interstellar medium is accelerated and/or subject to hydrodynamical instabilities, which reduce the scattering of Lyα. Concluding remarks take the form of perspectives upon future developments, and the most pressing questions that can be answered by observation.