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We demonstrate that Cherenkov radiation can be manipulated in terms of operation frequency, bandwidth, and efficiency by simultaneously controlling the properties of drifting electrons and the photonic states supported by their surrounding media. We analytically show that the radiation rate strongly depends on the momentum of the excited photonic state, in terms of magnitude, frequency dispersion, and its variation vs the properties of the drifting carriers. This approach is applied to design and realize miniaturized, broadband, tunable, and efficient terahertz and far-infrared sources by manipulating and boosting the coupling between drifting electrons and engineered hyperbolic modes in graphene-based nanostructures. The broadband, dispersive, and confined nature of hyperbolic modes relax momentum matching issues, avoid using electron beams, and drastically enhance the radiation rate—allowing that over 90% of drifting electrons emit photons. Our findings open an exciting paradigm for the development of solid-state terahertz and infrared sources.