Soft, elastic, solvent-rich materials made from networks of aggregated colloidal particles are called particle gels. The networks may be regarded as being permanent or transient depending on whether the short-range attractive forces between the particles arise from strong irreversible bonding or weak reversible interactions. Understanding the relationships between the interparticle forces and the structure and rheology of particle gels is a challenging problem. This article shows how useful insight is being provided by Brownian dynamics simulations involving systems of spherical particles interacting with a combination of bonded and nonbonded interparticle potentials,