Emission from Gamma-ray bursts is thought to be powered mainly by synchrotron radiation from energetic electrons. The same electrons might scatter these synchrotron seed photons to higher (>10 GeV) energies, building a distinct spectral component (synchrotron self-Compton, SSC). This process is expected to take place, but its relevance (e.g., the ratio between the SSC and synchrotron emitted power) is difficult to predict on the basis of current knowledge of physical conditions at GRB emission sites. Very high-energy radiation in GRBs can be produced also by other mechanisms, such as synchrotron itself (if PeV electrons are produced at the source), inverse Compton on external seed photons, and hadronic processes. Recently, after years of efforts, very high-energy radiation has been finally detected from at least four confirmed long GRBs by the Cherenkov telescopes H.E.S.S. and MAGIC. In all four cases, the emission has been recorded during the afterglow phase, well after the end of the prompt emission. In this work, I give an overview, accessible also to non-experts of the field, of the recent detections, theoretical implications, and future challenges, with a special focus on why very high-energy observations are relevant for our understanding of Gamma-ray bursts and which long-standing questions can be finally answered with the help of these observations.