The need for improved prediction of clinical response is driving the development of cancer models with enhanced physiological relevance. A new concept of 'precision biomaterials' is emerging, encompassing patient-mimetic biomaterial models that seek to accurately detect, treat and model cancer by faithfully recapitulating key microenvironmental characteristics. Despite recent advances allowing tissue-mimetic stiffness and molecular composition to be replicated in vitro, approaches for reproducing the 3D fibre architectures found in tumour extracellular matrix (ECM) remain relatively unexplored. Although the precise influences of patient-specific fibre architecture are unclear, we summarize the known roles of tumour fibre architecture, underlining their implications in cell-matrix interactions and ultimately clinical outcome. We then explore the challenges in reproducing tissue-specific 3D fibre architecture(s) in vitro, highlighting relevant biomaterial fabrication techniques and their benefits and limitations. Finally, we discuss imaging and image analysis techniques (focussing on collagen I-optimized approaches) that could hold the key to mapping tumour-specific ECM into high-fidelity biomaterial models. We anticipate that an interdisciplinary approach, combining materials science, cancer research and image analysis, will elucidate the role of 3D fibre architecture in tumour development, leading to the next generation of patient-mimetic models for mechanistic studies and drug discovery.