The modification of a variety of biomaterials and medical devices often encompasses the generation of biopassive and lubricious layers on their exposed surfaces. This is valid when the synthetic supports are required to integrate within physiological media without altering their interfacial composition and when the minimization of shear stress prevents or reduces damage to the surrounding environment. In many of these cases, hydrophilic polymer brushes assembled from surface-interacting polymer adsorbates or directly grown by surface-initiated polymerizations (SIP) are chosen. Although growing efforts by polymer chemists have been focusing on varying the composition of polymer brushes in order to attain increasingly bioinert and lubricious surfaces, the precise modulation of polymer architecture has simultaneously enabled us to substantially broaden the tuning potential for the above-mentioned properties. This feature article concentrates on reviewing this latter strategy, comparatively analyzing how polymer brush parameters such as molecular weight and grafting density, the application of block copolymers, the introduction of branching and cross-links, or the variation of polymer topology beyond the simple, linear chains determine highly technologically relevant properties, such as biopassivity and lubrication.