« This talk presents our recent insights to the complex dynamics involved in solid and deformable particle-laden flows using high-fidelity DNS simulations. We undertake a rigorous exploration of the interaction between a fixed and a freely moving angular polyhedron with an unbounded inertial flow. For a fixed Platonic polyhedron in the flow, we consider three different angular positions: face facing the flow, edge facing the flow, and corner facing the flow, to elucidate the effects of the particle angularity on the flow regime transitions. For freely settling particles in a quiescent fluid, our results elucidate the common transitional nature between the helical and oblique regimes, underlining the importance of the autorotation torque in the helical settling regime. Additionally, we explore the deformation, rheology, and diffusion of deformable elastic capsules in a simple shear flow within both Stokes and inertial regimes. Notably, we observe the formation of a novel bridge structure, prompted by purely hydrodynamic interactions between capsules. We also identify a novel diffusion regime for capsules in inertial flow, distinct from those observed in solid particle suspensions. »