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The first generation of hyperbolic metamaterials, metasurfaces, and naturally hyperbolic materials (HMMs) utilized the static and passive properties of their constituent metallic and dielectric components to achieve intriguing macroscopic behavior, such as imaging and focusing of light below the diffraction limit and the broadband modification to the rate of spontaneous emission. While promising, and operating from RF frequencies to the ultraviolet, many potential applications of early HMMs were spoiled by inflexible operation and dissipation losses. Recently, the use of dynamically tunable and active constituent materials has increased, guiding HMMs into more functional regimes. In this review we survey the state-of-the-art of tunable and active electromagnetic HMMs. Based on a firm theoretical foundation, we review the most recent experimental work on hyperbolic dispersion endowed with a tunable or active character. Additionally, we review proposed ideas that may inspire new experimental work and offer a comparison to other photonic platforms.