An optical micro/nanofiber (MNF) is a quasi-one-dimensional free-standing optical waveguide with a diameter close to or less than the vacuum wavelength of light. Combining the tiny geometry with high-refractive-index contrast between the core and the surrounding, the MNF exhibits favorable optical properties such as tight optical confinement, strong evanescent field, and large-diameter-dependent waveguide dispersion. Meanwhile, as a quasi-one-dimensional structure with extraordinarily high geometric and structural uniformity, the MNF also has low optical loss and high mechanical strength, making it favorable for manipulating light on the micro/nanoscale with high flexibility. Over the past two decades, optical MNFs, typically being operated in single mode, have been emerging as a miniaturized fiber-optic platform for both scientific research and technological applications. In this paper, we aim to provide a comprehensive overview of the representative advances in optical MNFs in recent years. Starting from the basic structures and fabrication techniques of the optical MNFs, we highlight linear and nonlinear optical and mechanical properties of the MNFs. Then, we introduce typical applications of optical MNFs from near-field optics, passive optical components, optical sensors, and optomechanics to fiber lasers and atom optics. Finally, we give a brief summary of the current status of MNF optics and technology, and provide an outlook into future challenges and opportunities.