Portability, efficiency, and ease of coding are all important considerations in choosing the programming model for a scalable parallel application. The message-passing programming model is widely used because of its portability, yet some applications are too complex to code in it while also trying to maintain a balanced computation load and avoid redundant computations. The shared-memory programming model simplifies coding, but it is not portable and often provides little control over interprocessor data transfer costs. This paper describes an approach, called Global Arrays (GAs), that combines the better features of both other models, leading to both simple coding and efficient execution. The key concept of GAs is that they provide a portable interface through which each process in a MIMD parallel program can asynchronously access logical blocks of physically distributed matrices, with no need for explicit cooperation by other processes. We have implemented the GA library on a variety of computer systems, including the Intel Delta and Paragon, the IBM SP-1 and SP-2 (all message passers), the Kendall Square Research KSR-1/2 and the Convex SPP-1200 (nonuniform access shared-memory machines), the CRAY T3D (a globally addressable distributed-memory computer), and networks of UNIX workstations. We discuss the design and implementation of these libraries, report their performance, illustrate the use of GAs in the context of computational chemistry applications, and describe the use of a GA performance visualization tool.