Recent developments in scanning tunneling microscopy studies of the electronic properties of single-walled carbon nanotubes are reviewed. A broad range of topics focused on the unique electronic properties of nanotubes are discussed, including (a) the underlying theoretical description of the electronic properties of nanotubes; (b) the roles of finite curvature and broken symmetries in perturbing electronic properties; (c) the unique one-dimensional energy dispersion in nanotubes; (d) the nature of end states; (e) quantum size effects in short tubes; (f) the interactions between local spins and carriers in metallic systems (the Kondo effect); and (g) the atomic structure and electronic properties of intramolecular junctions. The implications of these studies for understanding fundamental one-dimensional physics and future nanotube device applications are discussed.