There are disclosed methods and apparatus for monitoring fluid flow along a conduit such as a well bore or a pipeline. A sensor optical fiber is disposed along the conduit, and an optical interrogator is used to launch probe light pulses into the fiber and to determine optical properties of probe light backscattered within the fiber, the properties being indicative of vibration as a function along the fiber. An analyzer is used to detect one or more vibration features moving along the conduit and to determine a measure of fluid flow based on the detected movement.