Raman spectroscopy is a versatile tool for acquiring molecular structure information. The incorporation of plasmonic fields has significantly enhanced the sensitivity and resolution of surface-enhanced Raman scattering (SERS) and tip-enhanced Raman spectroscopy (TERS). The strong spatial confinement effect of plasmonic fields has challenged the conventional Raman theory, in which a plane wave approximation for the light has been adopted. In this review, we comprehensively survey the progress of a generalized theory for SERS and TERS in the framework of effective field Hamiltonian (EFH). With this approach, all characteristics of localized plasmonic fields can be well taken into account. By employing EFH, quantitative simulations at the first-principles level for state-of-the-art experimental observations have been achieved, revealing the underlying intrinsic physics in the measurements. The predictive power of EFH is demonstrated by several new phenomena generated from the intrinsic spatial, momentum, time, and energy structures of the localized plasmonic field. The corresponding experimental verifications are also carried out briefly. A comprehensive computational package for modeling of SERS and TERS at the first-principles level is introduced. Finally, we provide an outlook on the future developments of theory and experiments for SERS and TERS.