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The destiny of very-low mass stars and brown dwarfs represents a fairly simple and straightforward problem of stellar evolution. Stars with masses below 0.3$\,M_\odot$ have fully convective interiors, and their structure is very nearly adiabatic. The interior structure is therefore nearly independent of the opacity. The physics of the equations of state under the relevant conditions is not simple but is well understood and the low central temperatures reduce the p-p chain to a simple set of nuclear reactions.
Why are there significant differences between various evolutionary calculations? Why do disagreements persist between the latest models and the most accurate observations? The cause is to be found in the treatment of the atmosphere as the surface boundary condition to the equations of stellar structure and evolution. Because their interior structure is adiabatic, the models of very-low mass stars are rather sensitive to the surface boundary condition. The latter depends mostly on surface opacities, where large uncertainties remain, and the treatment of radiative and convective energy transport in the atmosphere, which is often handled too casually. Accurate evolutionary tracks for brown dwarfs and a precise determination of the locus of the main sequence for M$\le 0.3\,$M$_\odot$ will follow from the availability of an extensive grid of non-gray atmospheres for these objects.
Nevertheless, the main features of brown dwarf evolution are firmly established. They will be discussed along with a comparison with observations.
