The isotropic exchange model (Heinberg-Dirac-Van Vleck, HDVV) is applicable when the ground terms of the constituent ions are orbitally non-degenerate. The presence of the orbital degeneracy of the metal ions in a high symmetry surrounding urges us to go beyond the conventional spin model and to consider the following key problems: 1) special non-Heisenberg forms of highly anisotropic orbitallydependent exchange interactions that are shown to result in a strong magnetic anisotropy; 2) local (on-site) interactions, like spin-orbit coupling and contributions of low symmetry crystal fields. In this talk we will summarize the basic concepts and some applications of the extended model of the exchange to molecular magnets[1]. The following questions will be considered: 1. HDVV model, basic mechanisms: kinetic and potential exchange. 2. Orbital degeneracy and matrix form of the exchange Hamiltonian-illustration for an s-p molecule, strong magnetic anisotropy. 3. Concept of the orbitally-dependent exchange, effective Hamiltonian of the kinetic exchange in a general form. The microscopic background, the interrelations between the parameters of the Hamiltonian and the internal parameters of the system including all relevant transfer integrals and fundamental intracenter interactions. Application of the irreducible tensor operator technique. Some non-trivial symmetry properties. 4. Cyano-bridged systems containing Mn(III) and Mn(II) ions - dimeric and trimeric units. Magnetic anisotropy. 5. Cyanide based pentanuclear single-molecule magnet Mn(III)2Mn(II)3 6. Cubic Re(II)4 Mn(II)4 cluster. 7. Spin canting in Co chain. Pseudo-spin-1/2 Hamiltonian and exchange anisotropy. 8. Trigonal bypiramide Ni3Os2 compounds.