I endeavour to provide a thorough overview of our current knowledge of galaxies and their evolution during the first billion years of cosmic time, corresponding to redshifts z > 5. After first summarizing progress with the seven different techniques which have been used to date in the discovery of objects at z > 5, I focus thereafter on the two selection methods which have yielded substantial samples of galaxies at early times, namely Lyman-break and Lyman-α selection. I discuss a decade of progress in galaxy sample selection at z ≃ 5 − 8, including issues of completeness and contamination, and address some of the confusion which has been created by erroneous reports of extreme-redshift objects. Next I provide an overview of our current knowledge of the evolving ultraviolet continuum and Lyman-α galaxy luminosity functions at z ≃ 5 − 8, and discuss what can be learned from exploring the relationship between the Lyman-break and Lyman-α selected populations.