Modern industry of advanced polyolefins extensively uses Group 4 metallocene and post-metallocene catalysts. High-throughput polyolefin technologies demand the use of heterogeneous catalysts with a given particle size and morphology, high thermal stability, and controlled productivity. Conventional Group 4 metal single-site heterogeneous catalysts require the use of high-cost methylalumoxane (MAO) or perfluoroaryl borate activators. However, a number of inorganic phases, containing highly acidic Lewis and Brønsted sites, are able to activate Group 4 metal pre-catalysts using low-cost and affordable alkylaluminums. In the present review, we gathered comprehensive information on MAO- and borate-free activating supports of different types and discussed the surface nature and chemistry of these phases, examples of their use in the polymerization of ethylene and α-olefins, and prospects of the further development for applications in the polyolefin industry.