Spatially resolved omics technologies are transforming our understanding of biological tissues. However, the handling of uni- and multimodal spatial omics datasets remains a challenge owing to large data volumes, heterogeneity of data types and the lack of flexible, spatially aware data structures. Here we introduce SpatialData, a framework that establishes a unified and extensible multiplatform file-format, lazy representation of larger-than-memory data, transformations and alignment to common coordinate systems. SpatialData facilitates spatial annotations and cross-modal aggregation and analysis, the utility of which is illustrated in the context of multiple vignettes, including integrative analysis on a multimodal Xenium and Visium breast cancer study.