Various differences and similarities between warm and cold frontogenesis are numerically modeled. The hydrostatic adiabatic Boussinesq primitive equations are integrated on a two-dimensional grid. The frontogenesis is forced by an along-front gradient of potential temperature and by a vertically sheared cross-front wind field. The model develops fronts with the proper vertical circulations, strengths, and slopes; more positive relative vorticity than negative relative vorticity is produced, and the frontal zone at the surface develops in a zone of convergence. Model results indicate that cold fronts will propagate faster than warm fronts and that the fronts will develop on the time scale of 1--3 days. Nonlinear advections brake the frontogenesis for cold fronts in the model and are almost entirely responsible for realistic frontogenesis of warm fronts in the model. Conceptual models of both warm and cold frontogenesis are developed which clarify the origin of the vertical circulation and some of the frontogenesis processes.