The structural chemistry and the resultant properties can be exquisitely controlled in the f-block elements because in both the 4f and 5f series the decrease in ionic radii is extraordinarily systematic. The 4f and 5f ions can be coordinated with six to twelve oxygen atoms yielding a vast range of coordination geometries. Structure-property correlations of lanthanide-containing materials are being heavily investigated owing in part to their potentially useful applications in magnetism, ion exchange, fluorescence, and optical properties. For actinides, the electronic configurations and magnetic properties are difficult to ascertain particularly because of orbital hybridization, relativistic effects, and narrow bandwidths. Exploration of this field is filled with multiple opportunities but also challenges. Furthermore, owing to the similarities in ionic radii and coordination environments between lanthanides and actinides, it is interesting to compare the chemistry of the f-block elements using solid-state chemistry techniques. In this present work, we probe the structural chemistry of f-block elements using tellurite as the ligand to address the aforementioned questions. The reason tellurite was chosen as the ligand in this study is due to the presence of stereochemically active lone-pair electrons on the TeIV centers and the large variability in the coordination environments that the tellurite anions play in the crystalline architecture of this family of compounds. Tellurite anions can be further interconnected to form dimers, trimers, and polymeric structures, which enable a variety of unusual structures to form. Hydrothermal reactions were conducted in the synthesis of f element-containing tellurite compounds. Single crystal X-ray diffraction and powder X-ray diffraction studies were performed to elucidate the structure of the novel products. A superconducting quantum interference device (SQUID) magnetometer was used for the magnetic behaviour studies. Energy-dispersive X-ray spectroscopy (EDS) techniques were utilized for the elemental analysis. Spectroscopic techniques like UV-vis-NIR were also applied to identify the oxidation states and electronic transitions for f elements. This dissertation is focused on crystal chemistry, structure-property relationships, and possible applications of the f-block element containing materials. More than 120 new lanthanide or actinide containing compounds were synthesized in this study. Lanthanide and actinide tellurites show remarkable structural diversity from a crystallographic point of view and atypical physical properties of these compounds were discovered. Materials with special physical properties, for example magnetic behavior (Chapter 2, 4) and electronic properties (Chapter 3, 5), are discussed. Cationic frameworks materials (Chapter 6, 7) with potential anion exchange abilities are also presented. Besides the physicochemical property studies, structural comparison between 4f-block compounds (Chapter 8), as well as between 4f and 5f compounds (Chapter 9, 10), are included in this dissertation.