The Lyman-α (Lyα) emission line has proven the most powerful tool by which to detect high-redshift galaxies, thanks to its high equivalent width and its convenient rest-frame wavelength. It is now widely used for galaxy evolution and star formation diagnostics. However, this line undergoes a complex radiation transport leading to doubtful interpretation of Lyα observations. This emission line will be the main tool of the JWST and the ELTs for probing structures at all epochs and characterizing the sources of cosmic reionization. However, a number of apparent inconsistencies need first to be understood.
We will see how detailed HST observations of the local analogs of high redshift Lyα emitters (LAEs) allow us to investigate the different Lyα escape mechanisms. Then, I will discuss the results of Lyα radiative transfer simulations that explain the variety of Lyα profiles, the difference between local and distant galaxies, and the inferred unifying scenario between LBGs and LAEs. Finally, I will present the first empirical estimate of the Lyα escape fraction and its evolution with redshift, and the implications for galaxy evolution and the reionization epoch. Throughout this talk, I will discuss the important implications of these results on Lyα-based observations and future surveys.