In concurrent and distributed systems, software components are expected to communicate according to predetermined protocols and APIs - and if a component does not observe them, the system's reliability is compromised. Furthermore, isolating and fixing protocol/API errors can be very difficult. Many methods have been proposed to check the correctness of communicating systems, ranging from compile-time to run-time verification; among such methods, session types have been applied for both static type-checking, and run-time monitoring. This work takes a fresh look at the run-time verification of communicating systems using session types, in theory and in practice. On the theoretical side, we develop a novel formal model of session-monitored processes; with it, we formulate and prove new results on the monitorability of session types, connecting their run-time and static verification - in terms of soundness (i.e., whether monitors only flag ill-typed processes) and completeness (i.e., whether all ill-typed processes can be flagged by a monitor). On the practical side, we show that our monitoring theory is indeed realisable: building upon our formal model, we develop a Scala toolkit for the automatic generation of session monitors. Our executable monitors can be used to instrument black-box processes written in any programming language; we assess the viability of our approach with a series of benchmarks.