The first organic metals were obtained based on tetrathiafulvalene. The most significant advance in the field of organic metals was the discovery of superconductivity. The first organic superconductors were obtained based on tetramethyltetraselenafulvalene. These facts demonstrate great importance of tetraselenafulvalenes and their precursors, diselenafulvenes, for materials sciences. Derivatives of 1,4-diselenafulvene and 1,4,5,8-tetraselenafulvalene are useful building blocks for organic synthesis and donor units for the preparation of charge-transfer complexes and radical ion salts, the construction of organic metals, superconductors, organic Dirac materials, semiconductors, ferromagnets, and other conductive materials. This review covers the literature on the design, synthesis, and application of 1,4,5,8-tetraselenafulvalenes and 1,4-diselenafulvenes and their tellurium analogs over the past 15–20 years. These two classes of compounds are interconnected, since the main part of methods for the synthesis of tetraselenafulvalenes is based on the diselenafulvene derivatives as starting compounds. Special attention is paid to the development of novel efficient synthetic approaches to these classes of compounds. Conducting properties and distinguishing features of materials based on tetraselenafulvalenes and their tellurium analogs as well as examples of materials with high conductivity are discussed.