The discovery of relic galaxies in our nearby Universe allow us to explore the physical conditions that took place at the early stages of galaxy formation (z>2) with unprecedented detail. In this talk, we will describe how these objects have been found, what is the physical motivation to explore them and what are the most relevant results we have learnt so far. In particular, in this seminar, we will focus on our recent publication in the journal Nature, where we study the globular cluster population of the massive compact relic galaxy NGC1277 using the Hubble Space Telescope. The analysis of its globular cluster population has confirmed the extraordinary nature of this object. This galaxy underwent  an early collapse phase but failed to evolve and accrete smaller satellite galaxies. The study of the globular cluster of this system (which has no similar counterpart in the near Universe) gives unique insights into the formation and evolutionary processes of the most massive galaxies.