The availability of continental and global-scale spatio-temporal geographical data sets and the requirement to efficiently process, analyse and manage them led to the development of the temporally enabled Geographic Resources Analysis Support System (GRASS GIS). We present the temporal framework that extends GRASS GIS with spatio-temporal capabilities. The framework provides comprehensive functionality to implement a full-featured temporal geographic information system (GIS) based on a combined field and object-based approach. A significantly improved snapshot approach is used to manage spatial fields of raster, three-dimensional raster and vector type in time. The resulting timestamped spatial fields are organised in spatio-temporal fields referred to as space-time data sets. Both types of fields are handled as objects in our framework. The spatio-temporal extent of the objects and related metadata is stored in relational databases, thus providing additional functionalities to perform SQL-based analysis. We present our combined field and object-based approach in detail and show the management, analysis and processing of spatio-temporal data sets with complex spatio-temporal topologies. A key feature is the hierarchical processing of spatio-temporal data ranging from topological analysis of spatio-temporal fields over boolean operations on spatio-temporal extents, to single pixel, voxel and vector feature access. The linear scalability of our approach is demonstrated by handling up to 1,000,000 raster layers in a single space-time data set. We provide several code examples to show the capabilities of the GRASS GIS Temporal Framework and present the spatio-temporal intersection of trajectory data which demonstrates the object-based ability of our framework.