This talk presents two aspects of our on-going research on drug delivery. (1) Drug transport through tissue to tumor/cancel sites. This is usually modeled as unsteady or time-fractional convection-diffusion problems in poroelasticmedia, for which (weak Galerkin) finite element methods and finite volume methods can be used. Besides efficiency and robustness, these methods are expected to respect mass conservation and positivity. (2) Drug release from within polymeric nanoparticles, for which topology could be employed for research of drug-polymer conjugation. More interestingly, in vitro experiments can be integrated with machine learning.