Collective behavior and self-organization are ubiquitous mechanisms in nature. From animate creatures, such as swarming insects, flocking birds and schooling fish, to inanimate natural processes such as sedimentation and cloud formation, these phenomena arouse the curiosity of physicists and engineers alike. Early studies using analytical models and experiments in the low Reynolds number helped shed the light on the intricacies of particle interactions, as in clouds or arrays of spheres. In the intermediate Reynolds number regime however, the unsteadiness introduced by the fluid inertia, coupled to the object dynamics, add to the complexity of the problem. Numerical methods become then the tool par excellence to solve for these dynamics. The goal of this thesis is to lay out the foundations for a better understanding of particle interactions in fluids. Namely, we investigate the two-dimensional dynamics of interacting particles in a viscous fluid, in the intermediate Reynolds number range. We develop a direct numerical scheme based on the Immersed Interface Method to simulate the coupling of the dynamics of freely moving objects with the surrounding fluid. The method is used to study the dynamics of arrays of cylinders settling under gravity, and how these dynamics depend on the number of particles and their initial separation. We then provide a simple force law model which accounts for the initial repulsive force experienced by any two adjacent cylinders, at close range. When the particle density is high, collisions are almost inevitable. To treat close range interactions and resolve the interstitial flow in the narrowing gap between particles or between a particle and a wall, we further extend the immersed interface method to take into account the lubrication effects. We solve Reynolds equations and use the analytical solution in the lubrication region. Doing so enables us to avoid ad hoc methods where an artificial repulsive force is added or two-dimensional collision equations are used with a modified coefficient of restitution.