Scanning tunneling microscopy, spectroscopy, and tight-binding calculations have been used to elucidate the unique structural and electronic properties of single-walled carbon nanotubes (SWNTs). First, the unique relationship between SWNT atomic structure and electronic properties, and the richness of structures observed in both purified and chemically etched nanotube samples are discussed. Second, a more detailed picture of SWNT electronic band structure is developed and compared with experimental tunneling spectroscopy measurements. Third. experimental and theoretical investigations of localized structures, such as bends and ends in nanotubes, are presented. Last, quantum size effects in nanotubes with lengths approaching large molecules are discussed. The implications of these studies and important future directions an considered.