Understanding the dynamical evolution of protoplanetary disks is of vital importance in modern astrophysics because many of these environments are deemed to evolve into planetary systems like our own. In recent years, ALMA observations of the dust component and CO emission unveiled the presence of substructures such as spiral arms, rings, and gaps, and indicated that protoplanetary disks have a very rich dynamical activity. However, it is not clear yet whether the observed features are signatures of planets in formation, given the complexity of the astrophysical processes taking place at each of the different disk scales.In this thesis, we focus our efforts on studying the m omentum transfer between different species and its effect on the disks evolution. Despite disks being poorly ionized, charged species can transfer energy and momentum from the magnetic field to the neutrals due to collisions, significantly affecting the dynamics. In addition, the aerodynamical coupling between dust particles and the gaseous component has significant consequences for the dust dynamics and evolution. Thus, collisions play an important role in affecting different processes related to accretion mechanisms, the growth of dust particles, and the planetesimal formation. We base our discussion on three publications that define the core of this research. We first introduce a framework to solve the momentum exchange between multiple species with particular emphasis on dust dynamics. We then use this framework to study the impact of the self-organization induced by the Hall effect on the dust evolution, and the linear and non-linear phase of the streaming instability. More specifically, we present an asymptotically and unconditionally stable numerical method to account for the momentum transfer between multiple species. We show that the scheme conserves momentum to machine precision and that its implementation in the publicly available code FARGO3D converges to the correct equilibrium solution. Aiming at studying dust dynamics, we use the implementation to address problems such as damping, damped sound waves, local and global gas-dust radial drift in a disk and linear streaming instability. We furthermore provide analytical or exact solutions to each of these problems considering an arbitrary number of species. We successfully validate our implementation by recovering the solutions from the different test problems to second- and first-order accuracy in space and time, respectively. From this, we conclude that our scheme is suitable, and very robust, to study the self-consistent dynamics of several fluids. In the field of non-ideal magnetohydrodynamics, we investigate the evolution of turbulence triggered by the magneto-rotational instability, including the Hall effect and considering vertically unstratified cylindrical dsk models. In the regime of a dominant Hall effect, we robustly obtain large-scale selforganized concentrations in the vertical magnetic field that remain stable for hundreds of orbits. For disks with initially only vertical net flux alone, we confirm the presence of zonal flows and vortices that introduce regions of super-Keplerian gas flow. Including a moderately strong net-azimuthal magnetic flux can significantly alter the dynamics, partially preventing the self-organization of zonal flows.For plasma beta-parameters smaller than 50, large-scale, near-axisymmetric structures develop in the vertical magnetic flux. In all cases, we demonstrate that the emerging features are capable of accumulating dust grains for a range of Stokes numbers.Finally, we study the linear and non-linear phase of the streaming instability. This instability is thought to play a central role in the early stages of planet formation by enabling the efficient bypass of several barriers hindering the formation of planetesimals. We recover linear and non-linear results from previous works considering only one-dust species, validating our developed framework to study dust dynamics. Treating dust as a pressureless fluid, we run non-linear shearing-box simulations of the streaming instability and compare our results with two different setups previously obtained with Lagrangian particles. Simulations with Stokes number of unity show an excellent agreement with those performed with particles. However, in the other test case, which has a ten times smaller Stokes number, convergence with resolution is not found. We conclude that further studies are required in other to address whether the pressureless fluid approach is suitable for studying the non-linear phase of the streaming instability. We furthermore present the first study exploring the efficiency of the linear streaming instability when a particle-size distribution is considered. We find that, for a given dust-to-gas mass ratio, the multi-species streaming instability grows on timescales much longer than those expected when only one dust species is involved. In particular, distributions that contain dust-to-gas density ratios close to unity lead to unstable modes that can grow on timescales comparable to, or larger than those of secular instabilities. We anticipate that processes leading to particle segregation and/or concentration can create favorable conditions for the instability to grow fast. Our findings may have important implications for a large number of processes in protoplanetary disks that rely on the streaming instability as usually envisioned for a unique dust species. Our results suggest that the growth rates of other resonant-drag-instabilities may also decrease considerably when multiple species are considered