Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops 1-6 . Quantitative descriptors of vascular networks are an active area of research 1, 2, 7 and often focus on a single spatial resolution. Simultaneously, topological data analysis (TDA) 8, 9 , the mathematical field that studies 'shape' of data, has expanded from theory to applications through advances in computation and machine learning integration. Fully characterising the geometric, spatial and temporal tissue organisation is challenging, and its quantification is necessary to assess treatment effects. Here we showcase TDA to analyse intravital and ultramicroscopy imaging modalities and quantify spatio-temporal variation of twists, loops, and avascular regions (voids) in 3D vascular networks. We propose two topological lenses to study vasculature which capture inherent multi-scale organisation and vessel connectivity invisible to existing methods. This topological approach validates and quantifies known qualitative trends; specifically, dynamic changes in tortuosity and loops in response to antibodies that modulate vessel sprouting. Using these topological descriptors, we show further how radiotherapy alters the structure of tumour vasculature. Topological data analysis offers great potential for relating the form and function of vascular networks, and proposing novel biomarkers for tumour progression and treatment.Introduction. The advent of high resolution imaging techniques has driven the development of reconstruction algorithms, which generate exquisitely detailed 3D renderings of biological tissues, such as tumour vascular networks 10,11 . Analyses of these images have quantified structural features and shape, including vessel density, number of vessels and branch points 7 , fractal dimension 12 , and lacunarity 13 , and highlighted their relevance for monitoring disease progression 14,15 and treatment 6 . Tumours may contain regions of high and low vessel density 2 , the latter corresponding to vascular voids which are associated with tumour hypoxia and necrosis, and lead to reduced survival in patients and poor responses to therapy 2 . Artificial intelligence and machine learning algorithms represent the state-of-the-art for learning how to segment images; we employ them here.