Tip-enhanced near-field Raman microscopy spectroscopy is a scanning probe technique that is capable of providing vibrational spectroscopic information on single nanoobjects and surfaces at (sub-) nanometer spatial resolution and high detection sensitivity. In this review, we first illustrate the physical principle of optical nanoantennas used in tip-enhanced near-field Raman microscopy and tip-enhanced Raman scattering (TERS) to efficiently couple light to Raman excitations on nanometer length scales. Although the antennas' electric near-field distributions are commonly understood to determine the spatial resolution, recent experiments showing subnanometer-resolved optical images put this understanding into question. This is because such images enter a regime in which classical electrodynamical descriptions might no longer be applicable and quantum plasmonic and atomistic effects could become relevant. After summarizing the current understanding of plasmonic phenomena at extremely short length scales, we discuss the different mechanisms contributing to the signal enhancement. In addition to the known contributions from electric-field and chemical enhancement, several new models have been proposed very recently that could provide important guidelines for the optimization of TERS experiments. We then review recent developments in the areas of antenna design, fabrication, and characterization. Finally, we briefly highlight recent applications to illustrate future directions of tip-enhanced near-field Raman microscopy and TERS.