In this thesis I explore some of the brightest transient phenomena we observe in the highnenergy sky. I consider some of the observational difficulties we encounter in studying these highly variable sources, in particular the importance of the level of photon statistics, especially in the difficult region that sits between 10 and 100 GeV, where we have the overlap between the energy domain of space telescopes and the energy range more suited to ground-based Cherenkov telescopes. The specific sources I study here belong to various classes of gamma-ray emitters: Active Galactic Nuclei (AGN), compact binaries, and powerful flare events in the Sun's magnetosphere. The first chapter provides an introduction to the field of high energy gamma-ray astronomy. There, I cover the basic gamma-ray emission mechanisms and give an overview of the sources that I have investigated as well as a description of the telescopes and instruments involved in my gamma-ray observations of these sources. The second and third chapters discuss the work I have done together with colleagues in the H.E.S.S. Collaboration to enable the delivery of the first results from phase II of H.E.S.S. for two bright AGNs and the gamma-ray binary PSR B1259-63. The fourth chapter covers my work on analysing the gamma-ray emission from solar flares in order to put constraints on hadronic models of the are emission. The fifth chapter discusses the evidence for multiple components in the high energy spectrum of the blazar AGN called Mrk 501. The sixth chapter highlights the importance of the study of the cut-off region in bright gamma-ray sources detected by the Fermi- LAT, investigating also the possible improvements that will be brought about by the next generation of ground-based gamma-ray telescopes. Finally, the conclusions summarise my findings and explore future perspectives in the field.