Six new copper(ii) complexes with 2,2′:6′,2′′-terpyridine (4′-Rn-terpy) [1 (R1 = furan-2-yl), 2 (R2 = thiophen-2-yl), and 3 (R3 = 1-methyl-1H-pyrrol-2-yl)] and 2,6-di(thiazol-2-yl)pyridine derivatives (Rn-dtpy) [4 (R1), 5 (R2), and 6 (R3)] have been synthesized by a reaction between copper(ii) chloride and the corresponding ligand. The complexes have been characterized by UV-vis and IR spectroscopy, and their structures have been determined by X-ray analysis. The antiproliferative potential of copper(ii) complexes of 2,2′:6′,2′′-terpyridine and 2,6-di(thiazol-2-yl)pyridine derivatives towards human colorectal (HCT116) and ovarian (A2780) carcinoma as well as towards lung (A549) and breast adenocarcinoma (MCF7) cell lines was examined. Complex 1 and complex 6 were found to have the highest antiproliferative effect on A2780 ovarian carcinoma cells, particularly when compared with complex 2, 3 with no antiproliferative effect. The order of cytotoxicity in this cell line is 6 > 1 > 5 > 4 > 2 ≈ 3. Complex 2 seems to be much more specific towards colorectal carcinoma HCT116 and lung adenocarcinoma A549 cells. The viability loss induced by the complexes agrees with Hoechst 33258 staining and typical morphological apoptotic characteristics like chromatin condensation and nuclear fragmentation. The specificity towards different types of cell lines and the low cytotoxic activity towards healthy cells are of particular interest and are a positive feature for further developments. Complexes 1-6 were also tested in the oxidation of alkanes and alcohols with hydrogen peroxide and tert-butyl-hydroperoxide (TBHP). The most active catalyst 4 gave, after 120 min, 0.105 M of cyclohexanol + cyclohexanone after reduction with PPh3. This concentration corresponds to a yield of 23% and TON = 210. Oxidation of cis-1,2-dimethylcyclohexane with m-CPBA catalyzed by 4 in the presence of HNO3 gave a product of a stereoselective reaction (trans/cis = 0.47). Oxidation of secondary alcohols afforded the target ketones in yields up to 98% and TON = 630.