A major part of debugging, testing, and analyzing a complex software system is understanding what is happening within the system at run-time. Some developers advocate running within a debugger to better understand the system at this level. Others embed logging statements, even in the form of hard-coded calls to print functions, throughout the code. These techniques are all general, rough forms of what we call system monitoring, and, while they have limited usefulness in simple, sequential systems, they are nearly useless in complex, concurrent ones. We propose a set of new mechanisms, collectively known as a monitoring system, for understanding such complex systems, and we describe an example implementation of such a system, called IDebug, for the Java programming language.