Five new coordination polymers based on copper(I) halides or pseudohalide, [Cu2Br2(bpe)2] (1), [Cu2(CN)2(bpe)] (2), [Cu2Br2(bpp)2] (3), [Cu2I2(bpp)2]·(toluene) (4), and [Cu2I2(bpp)2]·(naphthalene) (5) (bpe = 1,2-bis(4-pyridyl)ethane, bpp = 1,3-bis(4-pyridyl)propane), have been synthesized by solvothermal methods and characterized by X-ray crystallography. All structures can be deconstructed into rhomboid Cu2X2 (X = Br, I, CN) dimers and flexible bridged dipyridyl ligands. In 1, two sets of (4,4) layers adopt the “diagonal−diagonal” 4-fold interpenetration mode, giving high catenation and generating a novel 2D → 3D interpenetrating framework. 2 is a 3D (3,6)-connected rutile-like net of 2-fold interpenetration. Each 3D rutile-like net consists of 2D flat [Cu2(μ3-CN)(μ-CN)] layers and bpe pillars. 3 is a 2D polycatenane formed by interlocking of 1D double-stranded tubular chains. 1D double-stranded tubular chains are also present in 4 and 5, similar to that found in 3; however, the presence of toluene or naphthalene guests prevents the 1D double-stranded tubular chains from interpenetration. The photoluminescent properties of 1 and 3 in the solid state have been studied.