Raman spectroscopy is a powerful experimental technique for characterizing molecules and materials that is used in many laboratories. First-principles theoretical calculations of Raman spectra are important because they elucidate the microscopic effects underlying Raman activity in these systems. These calculations are often performed using the canonical harmonic approximation, which cannot capture certain thermal changes in the Raman response. Anharmonic vibrational effects were recently found to play crucial roles in several materials, which motivates theoretical treatments of the Raman effect beyond harmonic phonons. While Raman spectroscopy from molecular dynamics (MD-Raman) is a well-established approach that includes anharmonic vibrations and further relevant thermal effects, MD-Raman computations were long considered to be computationally too expensive for practical materials computations. In this perspective article, we highlight that recent advances in the context of machine learning have now dramatically accelerated the involved computational tasks without sacrificing accuracy or predictive power. These recent developments highlight the increasing importance of MD-Raman and related methods as versatile tools for theoretical prediction and characterization of molecules and materials.