Transuranium elements, especially plutonium, play a special role in science and politics, due to their importance in both nuclear weapons and nuclear industry. However, owing to the radioactivity and toxicity of actinides there are severe restrictions regarding their storage, use, and disposal. One of the outcomes of this is the use of less toxic and less or non-radioactive surrogates for transuranium elements. The most central question is: do these surrogates actually mimic the chemistry of transuranics? In this present work we probe the structural chemistry of actinide diphosphonates to address this aforementioned question. In this research, the surrogates chosen are Ln(III) (Ln=La~Lu) for the An(III) (An= Pu, Am, Cm), Ce(IV), Th(IV) and U(IV) for Np(IV) and Pu(IV), and UO22+ for PuO22+. The ligands used in this research are methylenediphosphonic acid (C1P2) and phenylenediphosphonic acid (PhP2). Hydrothermal reactions, room temperature evaporations, as well as ionothermal reactions were conducted to study the interaction between these two ligands react with the transuranic elements and their surrogates, the difference and similairy between transuranic diphosphonates and their surrogates in terms of structural topology. To further illustrate the properties of those synthetic compounds, the following characterization techniques are used. The single crystal X-Ray Diffraction and powder X-Ray Diffraction experiments are conducted to explore the structure details of the products. For the elemental analysis, Inductively Coupled Plasma-Mass Spectrum (ICP-MS) and Energy-dispersive X-ray spectroscopy (EDS) techniques are utilized. Spectroscopic techniques like UV-vis-NIR are applied to identify the oxidation states for actinide elements.  As a result, in total 99 diphosphonate compounds were synthesized to fulfill this task. The structural types vary from zero-dimensional clusters, one-dimensional chains, two-dimensional layers to three-dimensional frameworks. The oxidation states of those transuranic elements involved are from trivalent to hexavalent. Such results offer a great opportunity for a thorough comparison of transuranic elements with their surrogates in different structure topologies and oxidation states in the diphosphonate system. Besides the comparison study, many new actinide compounds were synthesized with special properties. For example, two chiral, porous uranium metheylenediphosphonates were crystallized with channels about 1nm×1nm wide, large enough to conduct ion-exchange with coordination complexes such as [Co(en)3]3+. The Bond Valence parameters for Pu(IV), Np(IV) and Np(VI) was calculated and reported to assist the study the chemistry of transuranic elements.