Single-wall carbon nanotubes (CNTs) were discovered in 1993 and have been an area of intense research since then. They offer the right dimensions to explore material science and physical chemistry at the nanoscale and are the perfect system to study low-dimensional physics and transport. In the past decade, more attention has been shifted toward making use of this unique nanomaterial in real-world applications. In this article, we focus on potential applications of CNTs in the high-performance logic computing area—the main component of the semiconductor industry. We discuss the key challenges for nanotubes to replace silicon in integrated circuits and review progress made in recent years on the material, device, and circuit integration development of CNT technology.