The field of thermoelectric research has undergone a renaissance and boom in the past two and a half decades, largely fueled by the prospect of engineering electronic and phononic properties in nanostructures, among which semiconductor nanowires (NWs) have served both as an important platform to investigate fundamental thermoelectric transport phenomena and as a promising route for high thermoelectric performance for diverse applications. In this Review; we provide a comprehensive look at various aspects of thermoelectrics of NWs. We start with a brief introduction of basic thermoelectric phenomena, followed by synthetic methods for thermoelectric NWs and a summary of their thermoelectric figures of merit (ZT). We then focus our discussion on charge and heat transport, which dictate thermoelectric power factor and thermal conductivity, respectively. For charge transport, we cover the basic principles governing the power factor and then review several strategies using NWs to enhance it, including earlier theoretical and experimental work on quantum confinement effects and semimetal-to-semiconductor transition, surface engineering and complex heterostructures to enhance the carrier mobility and power factor, and the recent emergence of topological insulator NVVs. For phonon transport, we broadly categorize the work on thermal conductivity of NWs into five different effects: classic size effect, acoustic softening, surface roughness, complex NW morphology, and dimensional crossover. Finally, we discuss the integration of NWs for device applications for thermoelectric power generation and cooling. We conclude our review with some outlooks for future research.