In optoelectronic devices such as solar cells and photodetectors, a portion of electron-hole pairs are generated as so-called hot carriers with an excess kinetic energy that is typically lost as heat. The long standing aim to harvest this excess energy to enhance device performance has proven to be very challenging, largely due to the extremely short-lived nature of hot carriers. Efforts thus focus on increasing the hot carrier relaxation time, and on tailoring heterostructures that allow for hot-carrier extraction on short time-and length-scales. Recently, semiconductor nanowires have emerged as a promising system to achieve these aims, because they offer unique opportunities for heterostructure engineering as well as for potentially modified phononic properties that can lead to increased relaxation times. In this review we assess the current state of theory and experiments relating to hot-carrier dynamics in nanowires, with a focus on hot-carrier photovoltaics. To provide a foundation, we begin with a brief overview of the fundamental processes involved in hot-carrier relaxation, and how these can be tailored and characterized in nanowires. We then analyze the advantages offered by nanowires as a system for hot-carrier devices and review the status of proof-of-principle experiments related to hot-carrier photovoltaics. To help interpret existing experiments on photocurrent extraction in nanowires we provide modeling based on non-equilibrium Green's functions. Finally, we identify open research questions that need to be answered in order to fully evaluate the potential nanowires offer towards achieving more efficient, hotcarrier based, optoelectronic devices.