Lyman alpha emitting high-redshift galaxies offer insights into galaxy formation processes in the young universe. Moreover, they can be used to address cosmological questions regarding the “Epoch of Reionisation” and the nature of dark energy. In my talk I will show how integral field spectroscopy (IFS) is a viable observational technique for such studies. In particular, I will detail how we use IFS data to understand Lyman alpha escape mechanisms in a sample of nearby high-redshift analogues. I will then show how we use the revolutionary IFS instrument MUSE for conducting surveys of Lyman emitting galaxies in the redshift range 3 < z < 6. Here I will provide an overview over the latest results from those campaigns, with a particular focus on luminosity function studies. My talk will conclude with new (preliminary) results from a 17.5 hour MUSE integration of an extremely luminous extended z=3.1 Lyman alpha emitter known as ‘Lyman Alpha Blob 1’.