The phase diagram of manganites combines magnetic, orbital, lattice and charge ordering. We underline the essential role of strong cooperative Jahn-Teller interactions in selecting the magnetic structure and fine tuning by external parameters. First, the realistic Jahn-Teller distortions is LaMnO(3) controls the orbital order and consistently explain the layered antiferromagnetic ordering. Secondly, the phase diagram of half-doped manganites of the family La(0.5)Ca(0.5)MnO(3) can be reproduced, with the observed ferromagnetic, charge-ordered (CE) antiferromagnetic and paramagnetic insulating phases. RI Grilli, Marco/C-6309-2009; Fratini, Simone/A-4692-2009