Many types of geospatial analyses are computationally complex, involving, for example, solution processes that require numerous iterations or combinatorial comparisons. This complexity has motivated the application of high performance computing (HPC) to a variety of geospatial problems. In many instances, HPC assumes even greater importance because complexity interacts with rapidly growing volumes of geospatial information to further impede analysis and display. This chapter briefly reviews the underlying need for HPC in geospatial applications and describes different approaches to past implementations. Many of these applications were developed using hardware systems that had a relatively short life-span and were implemented in software that was not easily portable. More promising recent approaches have turned to the use of distributed resources that includes cyberinfrastructure as well as cloud and fog computing.