The most common model used for representing the evolution with age of the oceanic lithosphere is the 'plate model' where the temperature is set at a fixed depth, called the base of the plate. This 'base of the plate' has no physical meaning but this model provides a mathematical substitute for a system where small-scale convection occurs through instabilities growing at the base of the cooling lithosphere and becomes effective only below old ocean. Another possible view is that convection provides heat at the base of the lithosphere whatever the age of the overlying plate. This last process can be modeled by a Constant Heat flow Applied on the Bottom Lithospheric ISothetm (CHABLIS model). A good fit to the observables (bathymetry and geoid as function of age, and old age heat-flow) can be obtained both for plate and CHABLIS models in spite of an experimentally determined thermal expansion coefficient much larger than assumed in previous plate models. These models have important consequences for several geodynamic processes. The plate, at an age of 100 Ma is only 80 km thick for both models: melting above a hot-snot can then occur in the garnet-spine1 transition field without much plate thinning. In the plate model the subsidence is stopped at an age of about 80 Ma while, according to the CHABLIS model, several hundred meters of subsidence are expected after 100 Ma. Thus the two models predict quite a different long-term pattern of subsidence in the sedimentary basins. Finally, in the CHABLIS model, the global cooling of the mantle coming from cold material eroded by secondary convection at the base of the plates is considerably larger than in plate models: it amounts to 40%, the remaining 60% being due to the subduction process.