Dust grains are key players of the evolution of the dense interstellar medium. The grain size distribution varies locally, modifying the thermodynamics and the chemistry of molecular clouds, the opacity of collapsing protostellar cores and the coupling between the gas and the magnetic field, and the solid content to form planetesimals in protoplanetary disks. Magnetohydrodynamical models are commonly used to study the formation of stars and disks, but they generally do not capture the complexity of the interactions with the dusty component.

This complexity requires analytical and numerical methods that offer complementary levels of detail. In the first part of the talk, I present a multifluid approach that models the dynamics of a dust size distribution in interaction with the gas and the magnetic field. We explore its fundamental physics in the linear regime. We discuss the consequences of the coupling of the dust with the magnetic field on dust enrichment within the protostellar envelope and on magnetic braking (Verrier et al, in prep). In a second part of the talk, I present our new multifluid numerical method that allows us to simulate 3D dusty protostellar collapses (Verrier et al, 2025). This method is designed to capture all the coupling regimes between the gas and the neutral dust grains, including the terminal velocity regime (Lebreuilly et al, 2019). We find that millimeter dust grains enrich the first hydrostatic core and some locations of the envelope, promoted by the initial turbulence of the dense core, setting favourable conditions to early planet formation scenarios. Finally, we present perspectives that connect dust dynamics in turbulence and dust growth.