Spatially resolved transcriptomics (SRT) studies are becoming increasingly common and increasingly large, offering unprecedented opportunities to characterize the spatial and functional organization of complex tissues. In this talk, I will present two methods to address these challenges for dissecting heterogeneity in cell type spatial distribution and tissue structure. I will first introduce CARD for spatially informed cell type deconvolution. CARD takes advantage of the spatial correlation structure to enable accurate and robust deconvolution of spatial transcriptomics across technologies with different spatial resolutions and in the presence of mismatched scRNA-seq references. I will also introduce IRIS, for reference-informed integrative spatial domain detection. IRIS integrates multiple SRT tissue slices jointly, while explicitly considering correlation both within and across slices. This approach produces biologically interpretable spatial domains. We demonstrate the advantages of IRIS through in-depth analysis of six SRT datasets from different technologies across various tissues, species, and spatial resolutions. As a result, IRIS uncovers the fine-scale structures of brain regions, reveals the spatial heterogeneity of distinct tumor microenvironments, and characterizes the structural changes of the seminiferous tubes in the testis associated with diabetes. This is achieved with a speed and accuracy that existing approaches cannot match.