One-dimensional noble metal nanostructures are important components in modern nanoscience and nanotechnology due to their unique optical, electrical, mechanical, and thermal properties. However, their cost and scalability may become a major bottleneck for real-world applications. Copper, being an earth-abundant metallic element, is an ideal candidate for commercial applications. It is critical to develop technologies to produce 1D copper nanostructures with high monodispersity, stability and oxygen-resistance for future low-cost nano-enabled materials and devices. This article covers comprehensively the current progress in 1D copper nanostructures, most predominantly nanorods and nanowires. First, various synthetic methodologies developed so far to generate 1D copper nanostructures are thoroughly described; the methodologies are in conjunction with the discussion of microscopic, spectrophotometric, crystallographic and morphological characterizations. Next, striking electrical, optical, mechanical and thermal properties of 1D copper nanostructures are highlighted. Additionally, the emerging applications of 1D copper nanostructures in flexible electronics, transparent electrodes, low cost solar cells, field emission devices are covered, amongst others. Finally, there is a brief discussion of the remaining challenges and opportunities.