Two novel metal-organic frameworks (MOFs) [Cd-3(padc)(Hpadc)(H(2)padc)(H2O)](n)center dot nH(2)O (1, H(3)padc = pyrazole-3,5-dicarboxylic acid) and [Co-4(pidc)(2)(Hpidc)(4)(H2O)(3)](n)center dot 12nH(2)O (2, H(2)pidc = pyridine-2,5-dicarboxylic acid), that both crystallize in polar space groups, were solvothermally synthesized by using achiral N, O-coordinated ligands. Compound 1 consists of trinuclear Cd(II)-based units that are further bridged by the backbone of H(3)padc ligands to form a three-dimensional (3-D) (4,6)-connected fsc topology network, while compound 2 features two types of double-helical tubes with different chiralities connecting with each other alternatively to construct a typical 2-D (3,6)-connected kgd topology network. Importantly, 1 exhibits combined properties of photoluminescence (PL) and second harmonic generation (SHG), and represents the first noncentrosymmetric H(3)padc-based MOF that was obtained without any ancillary ligands. While 2 shows strong antiferromagnetic interactions between paramagnetic Co(II) centers, and the aqueous solution of 2 exhibits effective homogeneous photocatalysis properties under visible irradiation. Further, the mechanisms of the physical properties of 1 and 2 are discussed in detail.