Hexagonal boron nitride has been proposed as an excellent candidate to achieve subwavelength infrared light manipulation owing to its polar lattice structure, enabling excitation of low-loss phonon polaritons with hyperbolic dispersion. We show that strongly subwavelength hexagonal boron nitride planar nanostructures can exhibit ultra-confined resonances and local field enhancement. We investigate strong light-matter interaction in these nanoscale structures via photo-induced force microscopy, scattering-type scanning near-field optical microscopy, and Fourier transform infrared spectroscopy, with excellent agreement with numerical simulations. We design optical nano-dipole antennas and directly image the fields when bright- or dark-mode resonances are excited. These modes are deep subwavelength, and strikingly, they can be supported by arbitrarily small structures. We believe that phonon polaritons in hexagonal boron nitride can play for infrared light a role similar to that of plasmons in noble metals at visible frequency, paving the way for a new class of efficient and highly miniaturized nanophotonic devices.