The field of extragalactic astronomy is progressing rapidly but there is still much to understand and many questions that remain open. During recent years the Lyα emission line has come to the fore as a potentially very powerful astrophysical tool and is now routinely used to find galaxies at the very highest redshifts. However, using Lyα is complicated by the fact that it is a resonant line, which means that it undergoes radiative transfer as it travels through neutral hydrogen when escaping from galaxies. This makes Lyα observations very difficult to interpret, but it also means that Lyα can provide information about the neutral hydrogen in the universe, giving it the potential to, for instance, map the progression of the Epoch of Reionization—the large scale phase transition during which the universe went from being completely neutral to being dominated by ionized gas. 

In order to make the most of Lyα observations and extend its usefulness even further we need to understand exactly what kind of galaxies emit Lyα, and, by extension, which physical processes control its escape.  Even though Lyα is relatively easy to detect at high redshift we cannot study the details of the escape process there, due to the lack of additional information about the emitting galaxies.  In order to understand Lyα in detail then, we need to observe galaxies at much lower redshift where we can get more information. This is the main driver of the projects included in this thesis which focuses on furthering our understanding of Lyα using local universe observations. 

We find that Lyα escape is a strongly multivariate issue and that using simple machine learning techniques can both help us predict Lyα and determine what the main drivers of Lyα emission are. We present two studies focusing on multivariate prediction of both imaging and spectral observations of Lyα showing that it is, in general, possible to predict the total Lyα luminosity very well but that the equivalent width and the escape fraction still remain somewhat elusive. We show that the primary variables controlling of Lyα seem to be the production rate of Lyα photons and the ionization state of the surrounding gas. 

We also study the spatial distribution of extended Lyα halo emission in an effort to determine how important spatial scattering of Lyα is and whether the properties of halos change between low and high redshift. We find that halos at low redshift are remarkably consistent with high redshift results but that the extended emission most likely is not solely due to scattering of Lyα photons produced in the central galaxy but is also produced by faint stellar components at large radii, something not demonstrated before.

Lastly, we present a database of Lyα spectral profiles and use that dataset to examine the evolution of Lyα spectra as a function of redshift. The profiles show clear trends, with blueshifted emission becoming markedly less prominent at high redshifts. Using a prescription for the expected attenuation of the intergalactic medium, we show that the evolution in the profiles is consistent with the intrinsic line shape not evolving between redshift 0 and redshift 6. We also present work analyzing correlations of Lyα with both stellar population  and nebular gas properties in extensive detail shedding further light on what properties makes a galaxy a Lyα emitter.