Organizations that depend on mainframes for their mission critical applications have made extensive use of performance modeling for many years. After examining some of the reasons why performance modeling has been so important for mainframes, this article discusses a number of modeling problems that originally arose in the mainframe world, but are now of interest in a broader context. These problems include the analysis of multiprocessing (MPs and SMPs), clustering (shared DASD and parallel sysplex), logical partitioning (PR/SM), I/O subsystems (channels, cache), virtual storage interactions (paging and swapping) and goal mode scheduling.