Lyman alpha (Lya) emission provides a unique window into the high redshift Universe and can further our understanding of the physical processes involved. In this talk I will discuss two particular Lya observables: The Lya luminosity function and Lya spectra of galaxies. First, I will present a technique to compute the Lya luminosity function (LF) from the much better constrained UV continuum LF. This allows us to predict the evolution of the Lya LF with cosmic time, which can be relevant for understanding the Epoch of Reionization. Interestingly, our model predicts a very steep faint-end slope, which appears to have been confirmed by recent observations. Secondly, I will show results from our Lya radiative transfer calculations. In particular, I will discuss the "shell model", which is an only six-parameter subgrid-model representing a Lya emitting galaxy by a central luminous source surrounded by an outflowing shell of hydrogen and dust. In spite of its simplicity, the shell-model is highly successful in reproducing observed Lya spectra. Why this model can reproduce the complex scattering process through the multiphase interstellar medium is still unclear. After reviewing the free parameters of the "shell-model", I will describe common problems arising when shell-model parameters are extracted from observed Lya spectra. In order to overcome this, we propose a fully automated procedure, which allows for quantification of uncertainties and potential degeneracies. Time permitting, I will conclude with a brief comparison between the shell-model parameters and the ones of more complex multiphase medium.