Spatial transcriptomics has emerged as a groundbreaking tool for studying ligand-receptor interactions between cells, and such interactions exhibit spatial variability. To identify spatially variable ligand-receptor interactions (SVIs), we present SPIDER, which constructs cell-cell interaction interfaces and profiles, and identifies spatially variable interaction signals with multiple probabilistic models. We applied SPIDER to six datasets from four platforms of various tissues and obtained intriguing insights. First, we found the SPIDER-constructed interaction interfaces preserving the layer structure in the human dorsolateral prefrontal cortex samples. Similarly, on a human breast cancer dataset, we found interface clusters representing cancer in situ, invasive cancer, and tumor boundaries. Subsequently, applying SPIDER on mouse lung and human pancreatic ductal adenocarcinoma samples produces SVIs that correlate with cell-type markers, annotated clusters, and deconvoluted celltypes, suggesting that SVIs could represent distinct functions from celltypes. Additionally, on a developing mouse embryo dataset, SPIDER identifies distinct SVIs marking sub-brain regions, showing the potential of SVI in representing regional interactions. Investigation into the relation between spatially variable genes and SVIs suggests that the spatial variance of SVIs does not originate from ligands and receptors and that SVI and SVG are complementary in providing biological insights as SVIs enrich additional signaling pathways.