⎯The chemistry and technology of new versatile multipurpose catalytic systems developed and studied by the authors for the purposes of heterogeneous catalysis are reviewed. A theoretical background for a successful search for these new catalytic systems is based on an unconventional approach with emphasis on an essential role of branched-chain reaction mechanisms of heterogeneous catalysis previously developed by the authoring team. The catalytic systems under study are based on silica (aluminoborosilicate) glass-fiber amorphous matrices doped with various metals and manufactured as articles with various types of woven structure. The specific features of these glass-fiber woven catalytic systems, such as their structure, phase state of the matrix, manufacture and activation methods, design of catalytic reactors in which they operate, as well as production technologies and operation methods, make a compelling case to regard them as a new separate class of catalysts. As compared to conventional catalytic materials, these new catalysts are highly efficient in neutralizing industrial gas emissions, in contact stages of the production of nitric acid and sulfuric acid, in various reactions of catalytic hydrocarbon processing, in water purification from nitrate and nitrite contaminants, in catalytic heat generation, etc.