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Many different physical systems, such as granular materials, colloids, foams and emulsions exhibit a jamming transition where the system changes from a liquid-like flowing state to a solid jammed state as the packing fraction increases. These systems are often modeled using soft-core particles with repulsive contact forces. In this thesis we explore several different dynamical models for these kinds of systems, and see how they affect the behavior around the jamming transition. We investigate the effect of different types of dissipative forces on the rheology, and study how different methods of preparing a particle configuration affect their probability to jam when quenched. We study the rheology of sheared systems close to the jamming transition. It has been proposed that the athermal jamming transition is controlled by a critical point, point J, with certain scaling properties. We investigate this using multivariable scaling analysis based on renormalization group theory to explore the scaling properties of the transition and determine the position of point J and some of the critical exponents.