Single-walled carbon nanotubes (SWCNTs) have been attracting tremendous attention owing to their structure (chirality) dependent outstanding properties, which endow them with great potential in a wide range of applications. The preparation of chirality-pure SWCNTs is not only a great scientific challenge but also a crucial requirement for many high-end applications. As such, research activities in this area over the last two decades have been very extensive. In this review, we summarize recent achievements and accumulated knowledge thus far and discuss future developments and remaining challenges from three aspects: controlled growth, postsynthesis sorting, and characterization techniques. In the growth part, we focus on the mechanism of chirality-controlled growth and catalyst design. In the sorting part, we organize and analyze existing literature based on sorting targets rather than methods. Since chirality assignment and quantification is essential in the study of selective preparation, we also include in the last part a comprehensive description and discussion of characterization techniques for SWCNTs. It is our view that even though progress made in this area is impressive, more efforts are still needed to develop both methodologies for preparing ultrapure (e.g., >99.99%) SWCNTs in large quantity and nondestructive fast characterization techniques with high spatial resolution for various nanotube samples.