One of the main problems in chemotherapy using platinum drugs as anticancer agents is the resistance phenomenon. Synthesizing and evaluating valid alternative compounds is challenging. This review focuses on the last two years of progress in the studies of platinum (II)- and platinum (IV)-based anticancer complexes. In particular, the research studies reported herein focus on the capability of some platinum-based anticancer agents to bypass resistance to chemotherapy, which is typical of well-known drugs such as cisplatin. Regarding platinum (II) complexes, this review deals with complexes in trans conformation; complexes containing bioactive ligands, as well as those that are differently charged, all experience a different reaction mechanism compared with cisplatin. Regarding platinum (IV) compounds, the focus was on complexes with biologically active ancillary ligands that exert a synergistic effect with platinum (II)-active complexes upon reduction, or those for which controllable activation can be realized thanks to intracellular stimuli.