As a combination of fiber optics and nanotechnology, optical microfibers and nanofibers (MNFs) have been emerging as a novel platform for exploring fiber-optic technology on the micro/nanoscale. Typically, MNFs taper drawn from glass optical fibers or bulk glasses show excellent surface smoothness, high homogeneity in diameter and integrity, which bestows these tiny optical fibers with low waveguiding losses and outstanding mechanical properties. Benefitting from their wavelength- or sub-wavelength-scale transverse dimensions, waveguiding MNFs exhibit a number of interesting properties, including tight optical confinement, strong evanescent fields, evident surface field enhancement and large and abnormal waveguide dispersion, which makes them ideal nanowaveguides for coherently manipulating light, and connecting fiber optics with near-field optics, nonlinear optics, plasmonics, quantum optics and optomechanics on the wavelength- or sub-wavelength scale. Based on optical MNFs, a variety of technological applications, ranging from passive micro-couplers and resonators, to active devices such as lasers and optical sensors, have been reported in recent years. This review is intended to provide an up-to-date introduction to the fabrication, characterization and applications of optical MNFs, with emphasis on recent progress in our research group. Starting from a brief introduction of fabrication techniques for physical drawing glass MNFs in Section 2, we summarize MNF optics including waveguiding modes, evanescent coupling, and bending loss of MNFs in Section 3. In Section 4, starting from a “MNF tree” that summarizes the applications of MNFs into 5 categories (waveguide & near field optics, nonlinear optics, plasmonics, quantum & atom optics, optomechanics), we go to details of typical technological applications of MNFs, including optical couplers, interferometers, gratings, resonators, lasers and sensors. Finally in Section 5 we present a brief summary of optical MNFs regarding their current challenges and future opportunities.