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Ly{\alpha} emission, Ly{\alpha} absorption and MgII absorption are powerfultracers of neutral hydrogen. Hydrogen is the most abundant element in theuniverse and plays a central role in galaxy formation via gas accretion andoutflows, as well as being the precursor to molecular clouds, the sites of starformation. Since 21cm emission from neutral hydrogen can only be directlyobserved in the local universe, we rely on Ly{\alpha} emission, and Ly{\alpha}and MgII absorption to probe the physics that drives galaxy evolution at higherredshifts. Furthermore, these tracers are sensitive to a range of hydrogendensities that cover the interstellar medium, the circumgalactic medium and theintergalactic medium, providing an invaluable means of studying gas physics inregimes where it is poorly understood. At high redshift, Ly{\alpha} emissionline searches have discovered thousands of star-forming galaxies out to z = 7.The large Ly{\alpha} scattering cross-section makes observations of this linesensitive to even very diffuse gas outside of galaxies. Several thousand morehigh-redshift galaxies are known from damped Ly{\alpha} absorption lines andabsorption by the MgII doublet in quasar and GRB spectra. MgII, in particular,probes metal-enriched neutral gas inside galaxy haloes in a wide range ofenvironments and redshifts (0.1 < z < 6.3), including the so-called redshiftdesert. Here we review what observations and theoretical models of Ly{\alpha}emission, Ly{\alpha} and MgII absorption have told us about the interstellar,circumgalactic and intergalactic medium in the context of galaxy formation andevolution.

Lyman Alpha and MgII as Probes of Galaxies and their Environments