Blue jets are beams of blue light propagating from the tops of active thunderclouds up to altitudes of ∼50 km. They resemble tall trees with quasi-vertical trunk and filamentary branches. Their apparent speeds are in the range of 10 s to 100 s km/s. Other events, having essentially lower terminal altitudes (<26 km), are named blue starters. These phenomena represent the first documented class of upward electrical discharges in the stratosphere. Some of upward discharges, termed gigantic jets, propagate into the lower ionosphere at much higher speeds in the final phase. We describe salient features of the upward discharges in the atmosphere, give an assessment of the theories of their development, and discuss the consequences for the electrodynamics and chemistry of the stratosphere. We argue that this upward lightning phenomenon can be understood in terms of the bidirectional leader, emerging from the anvil.