  On the example of monolayer manganites we show that the theoretical ideas
developed long ago along the derivation of the spin t-J model from the Hubbard
model are nowadays very helpful in strongly correlated oxides with partly
filled degenerate orbitals. We analyze a realistic orbital t-J model for e_g
electrons in La_{1-x}Sr_{1+x}MnO_4 monolayer manganites, and discuss the
evolution of spin and orbital correlations under increasing doping by
performing exact diagonalization of finite clusters, with electronic kinetic
energy determined self-consistently at finite temperature by classical Monte
Carlo for t_2g spins. Several experimental results are reproduced.
