<p>Laser-excited electron motions allow the investigation of fundamental physical phenomena with unprecedented resolution in time, space and energy. The first step in most interactions between light and matter is the ultrafast response of electrons to impinging light, in which the electron dynamics is sensitive to the signatures of the driving light. As light can be tailored to carry custom angular momentum by imprinting it with characteristic structures of intensity, polarization or phase, the resulting structured light offers new opportunities to tailor and control the optical response of materials, far beyond the ability of conventional linearly or circularly polarized light. In this Review, we discuss recent progress at the intersection of the structured light and ultrafast physics communities alongside the underlying physics. Beyond these interesting fundamental considerations, we highlight the broad applications of structured light for investigating and controlling the dynamics of bound and free electrons, as well as extreme ultraviolet radiation, including in strong-field ionization, high harmonic generation and free-electron optical modulation.</p>