The challenge of CERN experiments at the Large Hadron Collider (LHC), which will collect data at rates in the range of PBs/year, requires the development of GRID technologies to optimize the exploitation of distributed computing power and the automatic access to distributed data storage. Several projects are addressing the problem of setting up the hardware infrastructure of a GRID, as well as the development of the middleware required to manage it: a working GRID should look like a set of services, accessible to registered applications, which will help cooperate the different computing and storage resources. As it happened for the World Wide Web, GRID concepts are in principle important not only for High Energy Physics (HEP): for this reason, GRID developers, while keeping in mind the needs of HEP experiments, are trying to design GRID services in the most general way. As examples, two applications are described: the CERN/ALICE experiment at the LHC and a recently approved INFN project (GPCALMA) which will set up a GRID prototype between several mammographic centres in Italy
