The Defense Advanced Research Projects Agency (DARPA) High Productivity Computing Systems (HPCS) program is focused on providing a new generation of economically viable high productivity computing systems for national security and for the industrial user community. The value of a high performance computing (HPC) system to a user includes many factors, such as execution time on a particular problem, software development time, direct hardware costs, and indirect administrative and maintenance costs. This special issue, which focuses on HPC productivity, brings together, for the first time, a series of novel papers written by several distinguished authors who share their views on this topic. The topic of productivity in HPC is very new and the authors have been encouraged to speculate. The goal of this first paper is to present an overarching context and framework for the other papers and to define some common ideas that have emerged in considering the problem of HPC productivity. In addition, this paper defines several characteristic HPC workflows that are useful for understanding how users exploit HPC systems, and discusses the role of activity and purpose benchmarks in establishing an empirical basis for HPC productivity.