Spectroscopic observations at extreme-and far-ultraviolet wavelengths have revealed systematic upflows in the solar transition region and corona. These upflows are best seen in the network structures of the quiet Sun and coronal holes, boundaries of active regions, and dimming regions associated with coronal mass ejections. They have been intensively studied in the past two decades because they are likely to be closely related to the formation of the solar wind and heating of the upper solar atmosphere. We present an overview of the characteristics of these upflows, introduce their possible formation mechanisms, and discuss their potential roles in the mass and energy transport in the solar atmosphere. Although past investigations have greatly improved our understanding of these upflows, they have left us with several outstanding questions and unresolved issues that should be addressed in the future. New observations from the Solar Orbiter mission, the Daniel K. Inouye Solar Telescope and the Parker Solar Probe will likely provide critical information to advance our understanding of the generation, propagation, and energization of these upflows.