Research contributions from our group have evinced significant progress in the solid-state chemistry of the rare-earth metal halides. This thesis presents results of the first extension of this progress into the scandium-tellurium and related ternary systems. The first evidence for the existence of metal-rich compounds in this system was the synthesis of Sc2Te. The internal metal-bonded features of the structure are double quasi-infinite chains of trans-edge-sharing metal octahedra, further augmented on each end by square-pyramids down the chain. These scandium chains have a blade-like shape and are spaced apart by tellurium atoms and a scandium zigzag chain. A second metal-rich compound was uncovered in Sc8Te3. Chains of trans-edge-sharing octahedra are again featured in much of the metal framework, but condensed into 2D sheets. In the Y8Te3 analog there is apparent disorder on some of the internal metal positions within the chains. The metal-richest compound synthesized in the scandium-tellurium system was Sc9Te 2. A higher degree of metal aggregation forms in four trans-edge-sharing metal octahedra chains condensed into 3 x 3 blocks, and linked together to form much thicker 2D sheets compared to Sc8Te3. Interesting distortions were analyzed with relationship to higher symmetry structures. The insertion of later transition metals into the earlier transition-metal framework results in the formation of the compounds Sc5Ni 2Te2, Sc6MTe2 (M = Mn, Fe, Co, Ni), Y5M2Te2 (M = Fe, Co, Ni) and the corresponding hydride, Y5Ni2TeH0.41(1). These compounds contain diverse sheet and columnar metal frameworks. Structural interrelationships among the many known ternary compounds are analyzed. The reaction of small amounts of aluminum into the scandium-tellurium systems revealed new substitution chemistry. The systems Sc5BxB' 3-x (B = Al or Ga; B' = Sn, Sb or Te) contained varied amounts of the triel elements (B) substituted on the same sites for either the tetrel, pnictide or chalcogenide (B'), respectively. Analysis of the synthesis and structure of these compounds was used to incrementally improve the continuously evolving scientific answers about recurring structural features and structure/property relationships in solids.