Analysing the genome, epigenome, transcriptome, proteome, and metabolome within the spatial context of cells has transformed our understanding of tumour spatiotemporal heterogeneity. Advances in spatial multi-omics technologies now reveal complex molecular interactions shaping cellular behaviour and tissue dynamics. This review highlights key technologies and computational methods that have advanced spatial domain identification and their pseudo-relations, as well as inference of intra- and inter-cellular molecular networks that drive disease progression. We also discuss strategies to address major challenges, including data sparsity, high-dimensionality, scalability, and heterogeneity. Furthermore, we outline how spatial multi-omics enables novel insights into disease mechanisms, advancing precision medicine and informing targeted therapies. KEY POINTS: Advancements in spatial multi-omics facilitate our understanding of tumour spatiotemporal heterogeneity. AI-driven multimodal models uncover complex molecular interactions that underlie cellular behaviours and tissue dynamics. Combining multi-omics technologies and AI-enabled bioinformatics tools helps predict critical disease stages, such as pre-cancer, advancing precision medicine, and informing targeted therapeutic strategies.