Recent studies suggest the existence of very massive stars (VMS) up to 300 solar masses in the local Universe. As this finding may represent a paradigm shift for the canonical stellar upper-mass limit of 150 solar masses, it is timely to evaluate the physics specific to VMS, which is currently missing. For this reason, we decided to construct a book entailing both a discussion of the accuracy of VMS masses (Martins), as well as the physics of VMS formation (Krumholz), mass loss (Vink), instabilities (Owocki), evolution (Hirschi), and fate (theory -- Woosley & Heger; observations -- Smith).