Gamma-Ray Bursts (GRBs) are brief events in the gamma-ray sky occurring at an average rate of a few per day. While they are on, they outshine every source of gamma-rays in the sky. In fact, they are the brightest electromagnetic explosions in the Universe. Until 11 years ago, they were undetected at any wavelengths other than gamma-rays, which provided poor directional information and hence no direct clues about their site of origin. The current interpretation of how this energy release is produced is that a large amount of energy is released in a short time (seconds or less) by the collapse of the core of a massive star or the merger of two compact stellar objects. This sudden energy liberation results in a fireball expanding at highly relativistic speed, which undergoes internal dissipation leading to gamma-rays, and later develops into a blast wave as it decelerates in the external medium, producing an afterglow which gets progressively weaker. The afterglows provide information about the nature of the GRB progenitor and the physical processes involved in these explosions. In this Thesis three GRBs are discussed where extensive follow-up observations could be performed. Thereby, this Thesis concentrates on the nature of the GRB progenitors, the phenomenology of the afterglows and the host galaxies. In Chapter 1 a brief introduction is given about this research field, followed by an overview of the Thesis. In Chapter 2 a broader summary is presented about the observational status of the field, including the most popular theoretical models. Chapter 3 contains information about the data gathering at various telescopes worldwide. Chapters 4 to 6 are devoted to certain aspects of GRB follow-up observations, namely the search for signatures of the nature of the GRB progenitors, the phenomenology and physical interpretation of the observed afterglow light as well as the nature of the GRB host galaxies. Chapter 7 finally summarizes the main work and results of the Thesis.