Towards the end of the second century BCE Philo of Byzantium, a.k.a. Philo Mechanicus, wrote what is held to be the first Engineering Compendium, in eight or nine parts. Three concern warfare, viewed theoretically: a technical treatise on catapult-design (Belopoiika), and two associated ones which survive only in (lengthy) epitome. United here under the title On Sieges, Paraskeuastika and Poliorketika address broader aspects of siege-warfare. First and primarily, withstanding a siege is the objective: cities must design and build towers, walls and gates in the most suitable way, stockpile and manage food and other strategic commodities, and resist a direct assault by men and machines. Then more briefly the perspective is reversed, with those who wish to conduct such an attack shown how to do so successfully. This is the work's first-ever complete translation into English, preceded by an Introduction on the writer and his work. The Commentary - the first since Garlan's in 1972 - aims to elucidate the multifarious matters arising: issues of text, translation, vocabulary, idiom; themes in the poliorcetic genre; archaeological and other substantive contexts.