  Overshooting occurs in stars when convective elements penetrate into adjacent
radiative zones. In the Sun, it leads to the so-called `tachocline' at the base
of the outer convection zone and this region is becoming a key ingredient of
the standard solar dynamo model as strong toroidal magnetic fields may be
generated there. However this overshoot is not predicted by the mixing-length
theory of convection where convective elements must stop at the border of a
convectively unstable region. I will review the main properties of this
convective overshoot in stellar interiors, with in particular its subtle
dependence with the thermal diffusion, and will present the most recent results
obtained from 2-D and 3-D direct numerical simulations (DNS) of penetrative
convection.
