Very-high-energy astrophysics studies the most energetic photons in the sky, allowing the exploration of violent and extreme non-thermal phenomena in the Universe. Significant advances in knowledge have been made in this field using ground-based imaging atmospheric Cherenkov telescopes (IACTs) as detectors, to study these physical processes in the Universe. This book reviews the progress in the field since the advent of the second generation IACTs around 2004. Going through the scientific highlights obtained by the three current instruments of this kind, H.E.S.S., MAGIC and VERITAS, operating now for more than 15 years, this book presents a state-of-the-art knowledge in four areas of modern astrophysics and cosmology, namely the origin of the cosmic rays, the physics of compact objects and their resulting relativistic outflows, gamma-ray cosmology, and the search for dark matter. Along with a detailed review of the outstanding scientific outcomes, a summary of the key technological developments that yielded the recognized success of the technique is also provided. This book is written for early-career academics in the fields of astrophysics, high energy physics and cosmology. At the same time, it can serve as a source of reference for the expert in the field.