Topological data analysis (TDA) is a novel and active field of research that combines concepts from pure and applied mathematics for quantifying shape in data. TDA has been successfully applied to both real-world data and mathematical models of biological processes. In this talk I will highlight two recent applications to synthetic spatial data from oncology. The first application is a case study of topological model selection in tumour-induced angiogenesis, the process in which blood vessel networks are formed during tumour growth. While many mathematical models of tumour-induced angiogenesis exist, significant challenges persist in objectively evaluating and comparing their outputs. We showcase a combination of TDA and approximate Bayesian Computation for parameter inference and model selection. In the second application I will present two relational TDA techniques that encode spatial relation in multispecies data, i.e. datasets with multiple subtypes of data points such as different cell types. We demonstrate that relational TDA features can extract biological insight, including dominant immune cell phenotype (an important predictor of patient prognosis) and parameter regimes of a data-generating model of tumour-immune cell interactions. Our relational TDA pipelines can be combined naturally with machine learning approaches for spatial data, such as graph neural networks.