Great interest in single-walled carbon nanotubes (SWCNTs) derives from their remarkable electrical, thermal, optical, and mechanical properties together with their lower density, which promise extensive and unique applications. Much progress has been achieved in the fundamental and applied investigations of SWCNTs over the past decade. At the same time, many obstacles still remain, hampering further development in this field. To clarify the emerging problems and to provide a comprehensive understanding of the field, we review the recent progress of research on the synthesis, structure, and properties of SWCNTs, in particular the SWCNT non-woven film, SWCNT rings, boron–nitrogen (B–N) co-doped SWCNTs (BCN-SWNTs), and individual SWCNTs. Some long-standing problems and topics warranting further investigations in the near future are addressed.