Electrostatic and hydrodynamic interactions have a profound impact on the structural and dynamic properties of a vast set of colloidal and biological systems. However, challenges are presented toward developing efficient numerical methods to describe these interactions due to their long-range and many-body nature. In this work, we develop several numerical models to describe electrostatic interactions with the consideration of the polarization effect in dry/deionized systems, to model hydrodynamic interactions and their coupling with thermal fluctuations for Brownian particles in suspensions, and to simulate the electrokinetic phenomena for charged particles suspended in ionic solutions. We then apply these efficient numerical approaches to several applications. First, we combine an evolutionary optimization strategy CMA-ES with a particle dynamics simulator based on the electrostatics models and successfully obtain the charges on granular polarizable particles based on a given set of experimental trajectories. Second, we examine the structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity and systematically study how lubrication, long-range hydrodynamics, particle volume fraction and shape affect the equilibrium structure and the diffusion behavior of these confined particles. The observations from this study suggest that the shape of biomolecules, particles, and polymers could determine their mobility and diffusion inside cells and tissues. Lastly, we examine the effect of electrostatic polarization on the dynamics of hydrodynamically interacting particles during sedimentation in unconfined and confined Stokes fluids. It is found that as particles agglomerate because of the electrostatic interactions and polarization effects, their collective motions are concomitantly modified by hydrodynamic interactions and fluid flows. It is also found that, when sedimenting in a confined geometry, dynamics of charged polarizable particles are strongly affected by the dielectric permittivities of the particle, fluid, and the confining geometry. These findings serve as a fundamental build up to understand the effect of hydrodynamic and electrostatic interactions on a wide range of applications including dynamics of biological entities in vascular environments and particle dynamics during water filtration and purification.