Dielectrics represent a new frontier for surface-enhanced Raman scattering. They can serve as either a complement or an alternative to conventional, metal-based SERS, offering key advantages in terms of low invasiveness, reproducibility, versatility, and recyclability. In comparison to metals, dielectric systems and, in particular, semiconductors are characterized by a much greater variety of parameters and properties that can be tailored to achieve enhanced Raman scattering or related effects. Light-trapping and subwavelength-focusing capabilities, morphology-dependent resonances, control of band gap and stoichiometry, size-dependent plasmons and excitons, and charge transfer from semiconductors to molecules and vice versa are a few examples of the manifold opportunities associated with the use of semiconductors as SERS-active materials. This review provides a broad analysis of SERS with dielectrics, encompassing different optical phenomena at the basis of the Raman scattering enhancement and introducing future challenges for light harvesting, vibrational spectroscopy, imaging, and sensing.