Technological advances have enabled lowinput RNA-sequencing, paving the way for assaying transcriptome variation in spatial contexts, including in tissues. While the generation of spatially resolved transcriptome maps is increasingly feasible, computational methods for analysing the resulting data are not established. Existing analysis strategies either ignore the spatial component of gene expression variation, or require discretization of the cells into coarse grained groups.To address this, we have developed SpatialDE, a computational framework for identifying and characterizing spatially variable genes. Our method generalizes variable gene selection, as used in population-and single-cell studies, to spatial expression profiles. To illustrate the broad utility of our approach, we apply SpatialDE to spatial transcriptomics data, and to data from single cell methods based on multiplexed in situ hybridisation (SeqFISH and MERFISH). SpatialDE enables the statistically robust identification of spatially variable genes, thereby identifying genes with known disease implications, several of which are missed by c o n v e n t i o n a l v a r i a b l e g e n e s e l e c t i o n . Additionally, to enable gene-expressed based histology, SpatialDE implements a spatial gene clustering model which we call "automatic expression histology," allowing to classify genes into groups with distinct spatial patterns.Technological advances have helped to miniaturize and parallelize genomics, thereby enabling high-throughput transcriptome profiling from low quantities of starting material, including in single cells. Increased experimental throughput has also fostered new experimental designs, where the spatial context of gene expression variation can now be directly assayed, which is critical for characterizing complex tissue architectures in multicellular organisms. The spatial context of gene expression is crucial for determining functions and phenotypes of cells 1,2 . Spatial expression variation can reflect communication between adjacent cells, or can be caused by cells that migrate to specific locations in a tissue to perform their functions.Several experimental methods to measure gene expression levels in a spatial context have been established, which differ in resolution, accuracy and throughput. These include the computational integration of single cell RNAseq data with a spatial reference dataset 3,4 , careful collection and recording of spatial location of samples 5 , parallel profiling of mRNA using barcodes on a grid of known spatial locations [5][6][7] , and methods based on multiplexed in situ hybridization 8,9 or sequencing 10-12 .A first critical step in the analysis of the resulting datasets is to identify the genes that exhibit spatial variation across the tissue. However, existing approaches for identifying highly variable genes 13,14 , as in single-cell RNA-sequencing (scRNA-seq) studies, ignore the spatial location and hence do not measure spatial variability ( Figure 1A). Alternatively, researchers have applied ANO...