Grid systems follow a new paradigm of distributed computing that enables the coordination of resources and services that are not subject to centralized control, can dynamically join and leave virtual pools, and are assigned to users by means of an explicit assignment functionality. The monitoring of a Grid is a multi-institutional and Virtual Organization (VO)-oriented service. It must deal with the dynamics, diversity, and geographical distribution of the resources available to Virtual Organizations, and the various levels of abstraction for modeling them. This paper presents the requirements, architecture and implementation of GridICE, a monitoring service for Grid systems. The suitability of this tool in real-life scenarios is analyzed and discussed.