Subwavelength- and nanometer-diameter glass nanofibers have been fabricated using a high-temperature taper-drawing process. As-drawn nanofibers show extraordinary uniformities in terms of diameter variation and surface roughness and are suitable for single-mode optical wave guiding. Measured optical losses of these nanofibers are typically below 0.1 dB/mm. Photonic devices such as linear waveguides, optical couplers and microrings assembled with nanofibers are also demonstrated. Our results show that taper-drawn glass nanofibers are promising building blocks for micro- and nano-scale photonic devices.