Using geometrical approach exposed in (Kersten et al. in J. Geom. Phys. 50:273–302,  and Acta Appl. Math. 90:143–178, ), we explore the Camassa–Holm equation (both in its initial scalar form, and in the form of 2×2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local and nonlocal).