Brillouin scattering in optical fiber describes the interaction of an electro-magnetic field (photon) with a characteristic density variation of the fiber. When the electric field amplitude of an optical beam (so-called pump wave), and another wave is introduced at the downshifted Brillouin frequency (namely Stokes wave), the beating between the pump and Stokes waves creates a modified density change via the electrostriction effect, resulting in so-called the stimulated Brillouin scattering. The density variation is associated with a mechanical acoustic wave; and it may be affected by local temperature, strain, and vibration which induce changes in the fiber effective refractive index and sound velocity. Through the measurement of the static or dynamic changes in Brillouin frequency along the fiber one can realize a distributed fiber sensor for local temperature, strain and vibration over tens or hundreds of kilometers. This paper reviews the progress on improving sensing performance parameters like spatial resolution, sensing length limitation and simultaneous temperature and strain measurement. These kinds of sensors can be used in civil structural monitoring of pipelines, bridges, dams, and railroads for disaster prevention. Analogous to the static Bragg grating, one can write a moving Brillouin grating in fibers, with the lifetime of the acoustic wave. The length of the Brillouin grating can be controlled by the writing pulses at any position in fibers. Such gratings can be used to measure changes in birefringence, which is an important parameter in fiber communications. Applications for this kind of sensor can be found in aerospace, material processing and fine structures.