Recent advances in apertureless scanning near-field optical microscopy (ASNOM) operating in the scattering-type scanning mode (sSNOM) are reviewed. Principles of ASNOM operation, technical solutions, distortions, and interference types characteristic of sSNOM-based instruments and theoretical models underlying the sSNOM technique are discussed. Methods for detecting the probing field effect on a sample under a tip (for example, thermal expansion) have been created; numerous studies have been conducted in the THz and microwave ranges. Material-contrast surface imaging is being successfully developed and nanoscale surface areas are being explored using spectroscopic methods. Progress in visualizing standing and running plasmon- and phonon-polariton waves over the surface of solid and 2D objects, including van-der-Waals materials and graphene, are presented. Hybridization of polariton states due to the interaction of carriers in a thin 2D object with those in a substrate has been discovered. Spatial resolution of ASNOM devices (1—20 nm) during the last 5—8 years has virtually remained the same.