Polaritons with hyperbolic dispersion are key to many emerging photonic technologies, including subdiffraction imaging, sensing and spontaneous emission engineering1, 2, 3, 4, 5, 6, 7, 8. Fundamental to their effective application are the lifetimes of the polaritons, as well as their phase and group velocities7, 9. Here, we combine time-domain interferometry10 and scattering-type near-field microscopy11 to visualize the propagation of hyperbolic polaritons in space and time, allowing the first direct measurement of all these quantities. In particular, we study infrared phonon polaritons in a thin hexagonal boron nitride8, 12, 13 waveguide exhibiting hyperbolic dispersion and deep subwavelength-scale field confinement. Our results reveal—in a natural material—negative phase velocity paired with a remarkably slow group velocity of 0.002c and lifetimes in the picosecond range. While these findings show the polariton's potential for mediating strong light–matter interactions and negative refraction, our imaging technique paves the way to explicit nanoimaging of polariton propagation characteristics in other two-dimensional materials, metamaterials and waveguides.