This is the first book dedicated to unidentified celestial gamma-ray sources. The launch of the Compton Gamma-Ray Observatory allowed the first all-sky surveys in gamma-rays, the most energetic form of electromagnetic radiation. The Energetic Gamma-Ray Experiment Telescope discovered more than 270 sources of high-energy protons, more than half of which are not identified with known celestial objects. Most of these objects belong to the Milky Way and more than one class of sources are present among the unidentified sources. Unravelling the nature of all these objects requires the combination of different sorts of instruments, like radio telescopes, optical telescopes, and X-ray satellites, together with the next generations of space and ground-based gamma-ray telescopes. This book presents the current knowledge on the subject and outlines strategies for identification of objects with current astronomical facilities. It provides a forward look by outlining the prospects of future generation gamma-ray telescopes. The contributions are detailed and represent valuable material for undergraduate and postgraduate astrophysics students and researchers in the field.