In this paper, we contrast four approaches for Grid computing, and discuss a computer systems approach in detail. This approach views a Grid as a distributed computer system, and its main concerns are systems abstractions and constructs, such as the Grid equivalents of computer architecture, address space, process, device, file system, user/developers interface. Following this methodology, we identified several essential issues, developed a Vega Grid systems architecture, and proposed several systems techniques such as Grid routers, Grid address spaces, Grid process (grip), Grid community (agora), and a Grid Service Markup Language (GSML) software suite. We evaluated the computer systems approach and the associated techniques by discussing an OSGA-compliant Grid system software implementation and a travel agency example.