This manuscript gathers my contributions focused on developing new mathematical and computational methods for analyzing biological flows as complex multiphysics and multiscale phenomena. The description of the underlying mechanisms stems from the basic principles of fluid dynamics and is translated into systems of partial or ordinary differential equations. The overall objective of this work is the study of these equations at the continuous and discrete levels, their coupling and the development of a reliable and efficient computational framework to implement various numerical methods to approximate the solutions to these problems. The numerical simulations incorporate realistic geometries, are thoroughly validated against experimental data and target specific biomedical applications. The first chapter focuses on three-dimensional models, in which the motion of a biofluid in a complex, realistic geometry is governed by the incompressible Navier-Stokes equations in a domain with inlet and outlet boundaries, the main application in view being the study of the cerebral venous network. The purpose of Chapter 2 is two-fold: (i) first, we present contributions towards the elaboration of several reduced 0d models describing the coupled dynamics of different biofluids in the eye- cerebral system; (ii) second, we describe a new splitting strategy for the numerical solving of coupled systems of partial and ordinary differential equations for fluid flows. In Chapter 3, the fluid dynamics description from the previous chapters is enriched to take into account the combined effects of flow and different structures, from a multiphysics perspective. The resulting framework is subsequently utilized for simulating blood flow in the aorta, in view of a specific biomedical application and for the numerical simulation of particulate flows, with an emphasis on the issue of how to handle contacts.