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The internal structure of stars is governed by hydrostatic support, the distribution of the chemical elements, the transport of energy by radiation and convection, and the liberation of energy by nuclear reactions. The evolution of stars is primarily determined by the changing composition due to the nuclear burning of elements in the central parts of the star, and the redistribution of the products of these reactions by mixing processes. The dominant mixing process is convection: it governs the extent of the mixed cores in moderate and large mass main sequence stars and their subsequent evolution, it mixes nuclear processed material into the envelopes of giants affecting the composition of material ejected into the interstellar medium, thereby affecting the chemical (and luminosity) evolution of galaxies. Understanding convection is essential if one is to understand the evolution of stars. Here I am concerned with convection in stellar cores and in particular with the extension of these cores by the penetration of convective motions into the surrounding stable layers affecting the internal structure and enlarging the chemically mixed region, which in turn affects the subsequent evolution. I briefly discuss a number of approaches to this problem: isochrone fitting of clusters and binary stars; simple theoretical models, the integral constraint, numerical simulation and what we can hope to get from asteroseismological observations of individual stars and of clusters and stellar groups.
