Rapid advances in optical microfiber and nanofibers (MNF) based sensors have been driven by powerful industries such as automotive, biomedical and defense, with the increasing demand for highly-sensitive, selective, nonintrusive, fast-response, compact and robust sensors that can perform in-situ measurements at remote and harsh environments. A diverse range of MNF based sensors have been developed for measuring refractive index, biochemical , temperature, current, displacement, bend, surface, acceleration, force, rotation, acoustic, electric field and magnetic field. Given the growing interest for this exciting area of scientific research, new designs are emerging continuously at a fast pace. This paper attempts to provide a comprehensive review of all MNF based sensors reported to-date. Sensors are divided according to their morphology and measurand.