Nanoparticles promise to improve the treatment of cancer through their increasingly sophisticated functionalisations and ability to accumulate in certain tumours. Yet recent work has shown that many nanomedicines fail during clinical trial. One issue is the lack of understanding of how nanoparticle designs impact their ability to overcome transport barriers in the body, including their circulation in the blood stream, extravasation into tumours, transport through tumour tissue, internalisation in the targeted cells, and release of their active cargo. Increased computational power, as well as improved multi-scale simulations of tumours, nanoparticles, and the biological transport barriers that affect them, now allow us to investigate the influence of a range of designs in biologically relevant scenarios. This presents a new opportunity for high-throughput, systematic, and integrated design pipelines powered by data and machine learning. With this paper, we review latest results in multi-scale simulations of nanoparticle transport barriers, as well as available software packages, with the aim of focussing the wider research community in building a common computational framework that can overcome some of the current obstacles facing efficient nanoparticle design.