Selected theoretical developments in modeling of deposition of sub-micrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We review deposition processes involving extended objects, with jamming and its interplay with in-surface diffusion yielding interesting dynamics of approach to the large-time state. Mean-field and low-density approximation schemes can be used in many instances for short and intermediate rimes, in large enough dimensions, and for particle sizes larger than few lattice units. Random sequential adsorption models are appropriate for higher particle densities (larger times). Added diffusion allows formation of denser deposits and leads to power-law large-lime behavior which, in one dimension (linear substrate, such as DNA), was related to diffusion-limited reactions, while in two dimensions (planar substrate), was associated with evolution of the domain-wall and defect network, reminiscent of equilibrium ordering processes.