The physics of mass transport within body compartments and across biological barriers differentiates cancers from healthy tissues. Variants of nanoparticles can be manufactured in combinatorially large sets, varying by only one transport-affecting design parameter at a time. Nanoparticles can also be used as building blocks for systems that perform sequences of coordinated actions, in accordance with a prescribed logic. We refer to these as Logic-Embedded Vectors (LEVs). Nanoparticles and LEVs are ideal probes for the determination of mass transport laws in tumors, acting as imaging contrast enhancers, and can be employed for lesion-selective delivery of therapy. Their size, shape, density and surface chemistry dominate convective transport in the bloodstream, margination, cell adhesion, selective cellular uptake, as well as sub-cellular trafficking and localization. As argued here, the understanding of transport differentials in cancer, termed ‘transport oncophysics', reveals a promising new frontier in oncology: the development of lesion-specific delivery particulates that exploit mass transport differentials to deploy treatment of greater efficacy and reduced side effects.