Polaritons, which are quasiparticles composed of a photon coupled to an electric or magnetic dipole, are a major focus in nanophotonic research of van der Waals (vdW) crystals and their derived 2D materials. For the variety of existing vdW materials, polaritons can be active in a broad range of the electromagnetic spectrum (meVs to eVs) and exhibit momenta much higher than the corresponding free‐space radiation. Hence, the use of high momentum broadband sources or probes is imperative to excite those quasiparticles and measure the frequency‐momentum dispersion relations, which provide insights into polariton dynamics. Synchrotron infrared nanospectroscopy (SINS) is a technique that combines the nanoscale spatial resolution of scattering‐type scanning near‐field optical microscopy with ultrabroadband synchrotron infrared radiation, making it highly suitable to probe and characterize a variety of vdW polaritons. Here, the advances enabled by SINS on the study of key photonic attributes of far‐ and mid‐infrared plasmon‐ and phonon‐polaritons in vdW and 2D crystals are reviewed. In that context the SINS technique is comprehensively described and it is demonstrated how fundamental polaritonic properties are retrieved for a range of atomically thin systems including hBN, MoS2, graphene and 2D heterostructures.