The current document is directed to virtualized PMUs provided by virtualization layers. The currently disclosed virtualized PMUs are decoupled from the underlying PMU hardware features of processors on which the virtualization layer executes. The decoupling is achieved, in part, by time multiplexing the underlying hardware PMU registers to provide a greater number of virtualized PMU registers than the number of hardware-PMU registers provided by at least some of the underlying hardware PMUs. The decoupling is also achieved by providing for monitoring, by the virtualized PMU registers, of computed processor events and approximated processor events in addition to the processor events monitored by the underlying hardware PMUs. In addition, the virtualized PMU registers are implemented, in certain implementations, to support a variety of different monitoring modes, including monitoring of processor events that occur only during execution of the virtualization layer and monitoring of hardware-thread-specific processor events.