In this paper, some recent contributions of both primitive equation ocean circulation models(OGCM) and idealized conceptual models to the understanding of the stability and variability properties of the ocean thermohaline circulation are reviewed. The typical results of a hierarchy of models have been represented in brevity. Emphasis has been put on the multiple steady states and variability from decadal/interdecadal timescale to centennial and millennial timescale of the world ocean thermohaline circulation.