Originality: Solves a much researched problem: how to give a compositional account of Ambients, a popular calculus for describing mobile agents. Rigour: Uses formal mathematical principles, including labelled transition systems and bismulation equivalences. Significance: First comprehensive semantic theory for the language of Ambients, a well-studied formal calculus for mobile agents. Impact: 91 citations (including conference version) in Google Scholar. Has spawned related work on calculi similar to Ambients. Conference version appeared in POPL, top rated long established conference, with acceptance rate less than 20%.