Spatial architecture in biological systems, such as human tissues, plays a crucial role in how they evolve and function over time. Direct measurement of past evolution is often infeasible in humans, however past dynamics leave behind a footprint on the spatial arrangement of cells. Despite this, the link between evolution within cell populations and their resulting spatial architecture remains largely unknown, and a deeper understanding of this relationship could help to elucidate past tissue dynamics, including early cancer evolution. Here we summarise recent advances, driven by spatial computational modelling, which exploit spatially resolved genomic data to reveal past evolution both in non-cancerous and cancerous human tissue. We first report on recent work [1] using spatial agent-based modelling in which we explore regenerative dynamics within normal human liver. Using spatial patterns of mitochondrial DNA mutations in tandem with agent-based modelling, we demonstrate for the first time the expansion dynamics of healthy liver cells in humans and show that long-lived progenitor cells, situated near the portal veins, drive punctuated expansions of liver cells over decade-long timescales. We next introduce a new study [2] in which we apply the same computational modelling framework to study sub-clonal evolution in colorectal cancer. Here, we developed a novel methodology using random walks to infer sub-clonal evolution in human tumour samples by quantifying high resolution spatial maps of tumour sub-population boundaries. We utilise this approach to describe the dynamics of mutant KRAS, BRAF and PIK3CA sub-populations in human colorectal cancer samples, and in doing so demonstrate how high resolution spatial patterns of sub-population mixing in tumours can provide insights into early cancer dynamics. Last, we introduce the next exciting direction for future spatial modelling research, where we investigate spatial evolutionary signatures in extracellular DNA (ecDNA) driven cancers. We discuss ongoing work to perform the first theoretical exploration into how spatial competition, coupled to random segregation of ecDNA fragments, drives oncogene amplification in these tumours. Combined, the new results presented in this talk demonstrate the knowledge which can be gained by leveraging the spatial context of cells, and provide a baseline for future spatial analyses of solid tissue.