Over the past three decades, extensive research activity on Brillouin scattering-based distributed optical fiber sensors has led to the availability of commercial instruments capable of measuring the static temperature/strain distribution over kilometer distances and with high spatial resolution, with applications typically covering structural and environmental monitoring. At the same time, the interest in dynamic measurements has rapidly grown due to the relevant number of applications which could benefit from this technology, including structural analysis for defect identification, vibration detection, railway traffic monitoring, shock events detection, and so on. In this paper, we present an overview of the recent advances in Brillouin-based distributed optical fiber sensors for dynamic sensing. The aspects of the Brillouin scattering process relevant in distributed dynamic measurements are analyzed, and the different techniques are compared in terms of performance and hardware complexity.