Abstract Motivation Spatially resolved transcriptomics (SRT) enables scientists to investigate spatial context of mRNA abundance, including identifying spatially variable genes (SVGs), i.e. genes whose expression varies across the tissue. Although several methods have been proposed for this task, native SVG tools cannot jointly model biological replicates, or identify the key areas of the tissue affected by spatial variability. Results Here, we introduce DESpace, a framework, based on an original application of existing methods, to discover SVGs. In particular, our approach inputs all types of SRT data, summarizes spatial information via spatial clusters, and identifies spatially variable genes by performing differential gene expression testing between clusters. Furthermore, our framework can identify (and test) the main cluster of the tissue affected by spatial variability; this allows scientists to investigate spatial expression changes in specific areas of interest. Additionally, DESpace enables joint modeling of multiple samples (i.e. biological replicates); compared to inference based on individual samples, this approach increases statistical power, and targets SVGs with consistent spatial patterns across replicates. Overall, in our benchmarks, DESpace displays good true positive rates, controls for false positive and false discovery rates, and is computationally efficient. Availability and implementation DESpace is freely distributed as a Bioconductor R package at https://bioconductor.org/packages/DESpace.