Electronic and magnetic structures of iron selenide compounds Ce₂O₂FeSe₂ (2212*) and BaFe₂Se₃ (123*) are studied by the first-principles calculations. We find that while all these compounds are composed of one-dimensional (1D) Fe chain (or ladder) structures, their electronic structures are not close to be quasi-1D. The magnetic exchange couplings between two nearest-neighbor (NN) chains in 2212*and between two NN two-leg-ladders in 123*are both antiferromagnetic (AFM), which is consistent with the presence of significant third NN AFM coupling, a common feature shared in other iron-chalcogenides, FeTe (11*) and K_yFe_2-xSe₂ (122*). In magnetic ground states, each Fe chain of 2212*is ferromagnetic and each two-leg ladder of 123*form a block-AFM structure. We suggest that all magnetic structures in iron-selenide compounds can be unified into an extended J₁–J₂–J₃ model. Spin-wave excitations of the model are calculated and can be tested by future experiments on these two systems.