Abstract Tropical cyclone (TC) structure and intensity are strongly modulated by interactions with deep-layer vertical wind shear (VWS)—the vector difference between horizontal winds at 200 and 850 hPa. This paper presents a comprehensive review of more than a century of research on TC–VWS interactions. The literature broadly agrees that a TC vortex becomes vertically tilted, precipitation organizes into a wavenumber-1 asymmetric pattern, and thermal and kinematic asymmetries emerge when a TC encounters an environmental sheared flow. However, these responses depend on other factors, including the magnitude and direction of horizontal winds at other vertical levels between 200 and 850 hPa, the amount and location of dry environmental air, and the underlying sea surface temperature. While early studies investigated how VWS weakens TCs, an emerging line of research has focused on understanding how TCs intensify under moderate and strong VWS (i.e., shear magnitudes greater than 5 m s−1). Modeling and observational studies have identified four pathways to intensification: vortex tilt reduction, vortex reformation, axisymmetrization of precipitation, and outflow blocking. These pathways may not be uniquely different because convection and vortex asymmetries are strongly coupled to each other. In addition to discussing these topics, this review presents open questions and recommendations for future research on TC–VWS interactions.