Metasurfaces control light propagation at the nanoscale for applications in both free-space and surface-confined geometries. However, all recent designs have exhibited concepts using geometrically fixed structures, or used materials with excessive propagation losses, thereby limiting potential applications. Here we show how to overcome these limitations using a reconfigurable hyperbolic metasurface comprising a heterostructure of isotopically enriched hexagonal boron nitride (hBN) in direct contact with a phase-change material (PCM), single crystal vanadium dioxide (VO2). Metallic and dielectric domains in VO2 provide spatially localized changes in the local dielectric environment to tune the wavelength of hyperbolic phonon polaritons (HPhPs) supported in hBN by a factor of 1.6. This contrasts with earlier work using surface phonon polaritons, where propagation could only be observed above a low-loss dielectric phase. We demonstrate the first realization of in-plane HPhP refraction, which obeys Snell’s law and the means for launching, reflecting and transmitting HPhPs at the PCM domain boundaries. To demonstrate practical applications of this platform, we show how hBN could be combined with either VO2 or GeSbTe glasses to make refractive nanophotonic waveguides and lenses. This approach offers control of in-plane HPhP propagation at the nanoscale and exemplifies a reconfigurable framework combining hyperbolic media and PCMs to design new optical functionalities including resonant cavities, beam steering and waveguiding.