  We provide a concise introduction to the symmetry approach to integrability.
Some results on integrable evolution and systems of evolution equations are
reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We
further describe non-abelian integrable equations, especially matrix (ODE and
PDE) systems. Some non-evolutionary integrable equations are studied using a
formulation of formal recursion operators that allows to study
non-diagonalisable systems of evolution equations.
