Four new rare-earth compounds, [Eu(NDC)1.5(DMF)2] (1), [Nd2(NDC)3(DMF)4].H2O (2), [La2(NDC)3(DMF)4].0.5H2O (3), and [Eu(BTC)(H2O)] (4), where NDC = 1,4-naphthalenedicarboxylate, BTC = 1,3,5-benzenetricarboxylate, and DMF = N,N-dimethylformamide, have been synthesized through preheating and cooling-down crystallization. Compounds 1-3 possess similar 2D structures, in which the NDC ligands link M(III) (M = La, Nd, and Eu) ions of two adjacent double chains constructed by NDC ligands and dinuclear M(III) building units. In compound 4, the Eu(III) ion is seven-coordinated by O atoms from six BTC ligands and one terminal water molecule in a distorted pentagonal-bipyramidal coordination environment. If the BTC ligand and the Eu(III) ion are regarded as six-connected nodes, respectively, the structure of compound 4 can be well described as a 3D six-connected net. Furthermore, compounds 1 and 4 exhibit strong red luminescence upon 355-nm excitation. Compound 2 displays interesting emissions in the near-IR region, and yellow (580 nm) pumping of this compound results in UV and intense blue emissions through an up-conversion process. The magnetic properties of compounds 1, 2, and 4 have been studied through measurement of their magnetic susceptibilities over the temperature range of 4-300 K.