Human Instrumentality Project (Rebuild)

The Human Instrumentality Project in the Rebuild of Evangelion series is mentioned by Kaworu Nagisa as a "rite of artificial evolution". The result is apocalyptic for life on Earth. It almost happened in Evangelion 2.0: You Can (Not) Advance when Evangelion Unit-01 awakened and caused the Near Third Impact. It was implied that Gendo planned this as he said at the end of the movie "We just have a little more to go to obtain our plan".

SEELE's Plan
SEELE's scenario was to use the Fourth Impact to kill all life on Earth which then would allow creatures with the "Fruit of Life" (probably the S² Engine) to be born. In Evangelion 3.0: You Can (Not) Redo, Gendo states that "They are born with the Fruit of Life" which most likely means they are Angels. It is also described as the "purification of souls" by SEELE but Gendo killed SEELE members by deactivating their monoliths. However their version of the Fourth Impact, along with their plan was stopped.

Gendo's Plan
Very little is known about Gendo's plan at the moment but it seems he still plans to renuite with Yui Ikari by unknown means. Part of his plan was to stop the Fourth Impact and the other part is the "Death of a God" (Kaworu Nagisa). The event almost went according to SEELE's scenario as said by Fuyutsuki after the Fourth Impact ended.

Relation to the "Impact" events
It seems that before Instrumentality can occur, an "impact" event is needed to kill all life on Earth. The end result would allow life forms born with the "Fruit of Life" to rise. The Near Third Impact would have been Gendo's scenario playing out while the Fourth Impact would have been SEELE's scenario.