The paper presents various transparency issues that have to be considered during development of object-oriented Grid applications based on virtual repositories. Higher-level transparencies, such as location, heterogeneity, fragmentation, replication, redundancy, indexing and service provider transparency assure new information processing culture greatly supporting the development, operation and maintenance of Grid database applications. The paper discusses some requirements for a virtual repository that is a kernel of a Grid database and a general architecture of such systems. The architecture is based on object-oriented updatable database views that serve, in particular, as adapters of local servers and integrators/mediators on the level of a global virtual repository. Finally, some issues of the development of Grid database applications are presented.