Title: The pi-calculus and its applications for localised runtime verification of distributed systems. Abstract: I will overview of the syntax and semantics of the core pi-calculus together with some variations such as the asynchronous pi-calculus, the polyadic pi-calculus and the distributed pi-calculus. I will cover both the reduction semantics and LTS semantics informally and present reasoning tools such as bisimulation equivalence. Finally, I will briefly discuss how we plan to use these formalisations to model runtime verification of distributed systems using localised migrating monitors.