This paper investigates rewriting logic as a suitable means to model the semantics of distributed and concurrent systems implemented using Monitoring Oriented Programming (MOP) frameworks. MOP tools close the gap between specification and implementation, allowing several formal specifications and concrete implementations to be combined into a single executing system. To address real-time monitoring of modern distributed applications, we recently proposed REAL-T, a reactive event-based distributed programming language with explicit support for distributions and time manipulation. REAL-T allows programmers to instrument distributed applications to monitor and enforce specific behavior. It also supports requirements of modern reactive applications (responsiveness, resiliency, elasticity and asynchronous communication). The REAL-T programming model is very flexible, making the semantic specifications very challenging.