Current limitations in typhoon forecasting are primarily attributed to insufficient understanding of mesoscale processes. To address this gap, this review synthesizes the current understanding of mesoscale waves in typhoons, including Vortex Rossby Waves (VRWs) and Typhoon-induced Gravity Waves (TGWs). It investigates their generation mechanisms and characteristics, and systematically examines the linkages between these waves and key typhoon structural features, including the eyewall, spiral rainbands, convective intensity, and (a) symmetric structure. Furthermore, the impact of these structural modifications on typhoon intensity is investigated, along with the statistical correlations between wave characteristics and typhoon intensity changes. The results show that: \mathrm{①} The theoretical frameworks for polygonal eyewall and inner spiral rainband formation have evolved from the TGW approach to that of VRWs. VRWs provide partial explanations for typhoon asymmetric structures and double-eyewall formation while representing one plausible mechanism for outer spiral rainbands. The changes in intensity induced by VRWs manifest through complex processes characterized by differing dynamical responses depending on (i) wave propagation directionality (tangential/radial), (ii) spatial domain (inner-core/outer region) and (iii) levels (mid-lower/upper) at (iv) different periods during the typhoon lifecycle phase (intensification/decay). \mathrm{②} The wave characteristics of TGWs (including amplitude, wavelength, period, and occurrence frequency) exhibit correlation with changes in typhoon intensity. TGWs, primarily excited by convection in the eyewall and spiral rainbands and rapidly propagating vertically, may serve as precursor signals for typhoon (rapid) intensification. \mathrm{③} Both VRWs and TGWs can drive the outward radial transport of momentum and heat within typhoons. Through wave-mean flow interactions, they modify local circulation and enhance typhoon symmetry, ultimately contributing to typhoon intensification (including rapid intensification). Some scientific challenges remain in applying VRWs and TGWs to improve fine-scale wind/precipitation distributions and advance the forecasting of changes in typhoon intensity. Current research underscores the necessity of integrating high-resolution numerical simulations with multi-platform coordinated observations to quantitatively analyze mesoscale wave-typhoon interactions, thereby identifying precursor signals for typhoon intensification, including rapid intensification. Tools such as wave spectrum analysis and wave energy flux diagnostics are instrumental in extracting early-warning indicators from both wave characteristics and energy transport perspectives. Advances in satellite and radar detection technologies will enable the validation of theoretical frameworks through multi-platform observational data, ultimately enhancing monitoring and forecasting capabilities for typhoon structural and intensity changes.