The community of people using vector processors is growing rapidly. First, within the United States, the National Science Foundation has established several vector supercomputer centers, and a large number of scientists in academe will be using these resources. Second, IBM has added a vector capability to its high-end mainframe system, and the widespread use of these systems will dramatically increase the community of people using vector processors. Finally, host of minicomputer manufacturers have added vector capability to their latest systems. So, as a result, there will likely be a reveal of interest in vectorization and some exciting additions to the associated technology. The intent of this paper is to provide many of these new users of vector processors with a high-level discussion of some of the fundamental aspects of vector processing.