The Lyα emission line is currently a leading tracer of star formation at cosmological distances. Since it becomes the strongest line in the optical-NIR window at redshift ≥ 2.1. Lyα proves an invaluable tool by which to detect galaxy populations at highest redshifts and a versatile mean for galaxy evolution diagnostics. However, with respect to these promising Lyα -based cosmological studies, number of inconsistencies have first to be understood to ensure proper interpretations. This is the main goal of the present work. Since typical high-z galaxies are very faint and detailed observations are difficult, we present an alternative approach which relies on observations of their local analogs using the Hubble space telescope to investigate the Lyα escape mechanisms. Then, we perform Lyα radiative transfer simulations in local and distant galaxies to understand the link between the different galaxy populations. Finally, we present the first empirical estimate of the Lyα escape fraction in a large sample of Lyα emitters in order to calibrate different Lyα -based cosmological quantities.