Dataspaces aim to remove upfront cost in the generation of the schema mappings that reconcile schematic heterogeneities, and to incrementally improve the generated mappings based on user feedback. The reconciliation of schematic heterogeneities is a crucial step for translating queries between a mediating schema and data sources. The generation of schema mappings depends on the elicitation of conceptually equivalent schema constructs and information on schematic heterogeneities. Furthermore, many dataspace operations manipulate associations between schemas, for example for generating a global schema to mediate user queries. With a view to minimizing upfront costs associated with understanding the relationships between schemas, many schema matching algorithms and tools have been developed for postulating equivalent schema constructs. However, they derive simple associations between schema constructs, and do not provide rich information on schematic heterogeneities. Without manual refinement, the elicitation of conceptually equivalent schema constructs and schematic heterogeneities may create uncertainties that must be managed.The schematic correspondences captures a wide range of one-to-one and many-to-many schematic heterogeneities. This thesis investigates the use of schematic correspondences as a central component in a dataspace management system. To support query evaluation in a dataspace in which relationships between schemas are represented using schematic correspondences, we propose a mechanism for automatically generating schema mappings from the schematic correspondences. We then characterise model management operators, which can underpin the bootstraping and maintenance of dataspaces, over schematic correspondences. To support the management of uncertainty in dataspaces, we propose techniques for quantifying uncertainty in the equivalence of schema constructs from evidence in the form of similarity scores and user feedback, and provide a flexible framework for incrementally updating the uncertainties in the light of new evidence.