The epoch of reionization at the infancy of the Universe is one of the observational frontiers of modern astronomy. It has been the key focus of numerous studies over the past decade. Through an impressive advancement of observational capabilities both on the ground and in space, these efforts have resulted in a tremendous gain of insight. Even though many questions about the early Universe are still unanswered, with more than 1000 galaxies currently known at redshifts greater than 6, i.e., less than one Gyr after the Big Bang, we understand the formation and life of the first galaxies better than ever before in terms of luminosities, stellar masses, sizes, colors, etc. I will present an observer's view of the galaxies at the epoch of reionization, describing the preferred tools used to study the high-redshift Universe, and the main insights these tools have let to in recent years. In particular, I will focus on the impact the Hubble Space Telescope's near-infrared imaging and spectroscopic capabilities has had on this field.