The Lyman-α line is currently one of our most important observational windows to the high/redshift Universe. With 68% of ionizing photons emitted inside HI sys- tems being reprocessed into Lyα, and HI being by far the most abundant neutral species in the Universe, it is clear that Lyα makes up a very high fraction of in- trinsic radiation from star/forming regions, AGN or other places, where hydrogen gets ionized and is dense enough to recombine. However, Lyα is a resonant tran- sition with a large interaction cross section, leading to complex radiative transfer effects which can strongly redistribute Lyα readiation both geometrically and in frequency space. These effects, it turns out, are not governed by one single cause, but by an intricate interplay between a number of competing factors including but not limited to dust content, HI column density, geometry and kinematics. Thus; while the strength of the Lyα line makes it possible to observe galaxies and sim- ilar scale systems at indeed very high redshifts, correct interpretation of these observations requires a detailed understanding of the inner workings of galaxy and the interplay of the factors mentioned above. Our knowledge of this is still incomplete, and the research presented here is part of a larger, joint effort to im- prove our knowledge of these effects, possibly benefiting the larger extragalactic astronomy community. In this thesis, I present the theory of the Lyα line and its radiative transfer in a neutral medium. I sketch the history of research in Lyα emitting galaxies as well as the current state of the field; before presenting my own contribution to it in the shape of a research paper which is currently, at the time of writing, under review at the Astrophysical Journal.