The studies on discharges in liquid dielectrics have been continuously gaining great attentions in the field of high voltage and insulation engineering. Profound understandings of the characteristics and mechanism of micro/nano-second pulsed discharge in liquids are prerequisites to the innovation and breakthrough of various cutting-edge applications, e.g., optimized electrical equipment design, deep ocean explorations, advanced material synthesis. In this review, we summarize the recent progress in the investigations of characteristics and mechanisms of micro/nano-second pulsed streamer discharge in liquid dielectrics. Fundamental characteristics of streamer discharge are elucidated including discharge modes and transition, branching characteristic, and breakdown. The contributing factors on the streamer characteristics, such as liquid conductivity, pressure, dissolved gas, impurities and additives, are analyzed. Prevailing mechanisms of initiation and propagation of streamer discharge in liquids as well as their application scenarios are discussed, including bubble theory, direct impact ionization, field molecular ionization, electrostriction, etc. Further, we expect the prospects and challenges of liquid discharge to enlighten fundamental researches and engineering applications in the relevant fields.