This review discusses the lattice Boltzmann-particle dynamics (LBPD) multiscale paradigm for the simulation of complex states of flowing matter at the interface between physics, chemistry, and biology. In particular, current large-scale LBPD simulations of biopolymer translocation across cellular membranes, molecular transport in ion channels, and amyloid aggregation in cells are described. Prospects are provided for future LBPD explorations in the direction of cellular organization, the direct simulation of full biological organelles, all the way up to physiological scales of potential relevance to future precision-medicine applications, such as the accurate description of homeostatic processes. It is argued that. with the advent of Exascale computing, the mesoscale physics approach advocated in this review may come to age in the next decade and open up new exciting perspectives for physics-based computational medicine.