The middle convolution is a motivic operation on local systems on punctured affine lines. The middle convolution, which was introduced by N. Katz, is a very powerful tool in algebraic geometry. It leads to motivic interpretations of rigid local systems and most of the known realizations of classical groups as Galois groups over Q (e.g., one obtains a much finer description of Belyi's results on classical groups as Galois groups). We give an outline of the main methods and explain the construction of a motivic local system whose monodromy lies dense in the simple algebraic group of type G2.