Modeling electrophoresis of peptides, proteins, DNA, blood cells and colloids is based on classical electrokinetic theory. The coupled field equations-Poisson, Navier-Stokes or Brinkman, and ion transport equations are solved numerically to calculate the electrophoretic mobilities. First, free solution electrophoretic mobility expressions are derived for weakly charged rigid bead arrays. Variables include the number of beads (N), their size (radius), charge, distribution (configuration), salt type, and salt concentration. We apply these mobility expressions to rings, rigid rods, and wormlike chain models and then apply the approach to the electrophoretic mobilities and translational diffusion constants of weakly charged peptides. It is shown that our bead model can predict the electrophoretic mobilities accurately. In order to make the method applicable at higher salt concentrations and/or to models consisting of larger sized subunits, account is taken of the finite size of the beads making up the model structure. For highly charged particles, it is also necessary to account for ion relaxation. This ion relaxation effect is accounted for by correcting "unrelaxed" mobilities on the basis of model size and average electrostatic surface, or "zeta" potential. With these corrections our model can be applied to the system with absolute electrophoretic mobilities exceeding approximately 0.20 cm2/kV sec and also models involving larger subunits. This includes bead models of duplex DNA. Along somewhat different lines, we have investigated the electrophoresis of colloidal particles with an inner hard core and an outer diffusive layer ("hairy" particles). An electrokinetic gel layer model of a spherical, highly charged colloid particle developed previously, is extended in several ways. The charge of the particle is assumed to arise from the deprotonation of acidic groups that are uniformly distributed over a portion (or all) of the gel layer. Free energy considerations coupled with Poisson-Boltzmann theory is used to calculate the change of the local pKa of the acidic groups depending on the local electrostatic environment. Based on the modeling of electrophoresis and viscosity, we predict that the thickness of the gel layer decreases as the salt concentration increases. And only the outermost portion of the gel layer is charged.