Rebuild of Evangelion follows basic canon from the original series, up until after the battle with Ramiel, where the timeline and events diverge. It is now 2015, fourteen years after the Second Impact, a cataclysmic event that occured in Antarctica that resulted in the melting of the south pole's ice and flooding of the world's coastal areas. The impact also changed the Earth's axis and rotation, disrupting the seasons.
After the outbreak and end of World War Three, the United Nations paramilitary organization known as NERV has built the Evangelions at the behest of SEELE, a shadowy concil of 13 people who are pulling the strings behing the UN and NERV. The Evangelions are being used to fight against the Angels, seemingly alien beings who sporadically attack humans. While their purpose seems to be random destruction, they all seek to come in contact with the Angel that the NERV facility in Tokyo III has imprisoned deep within Terminal Dogma, it's lowest level. Contact between this Angel, Lilith, and another Angel would result in the Third Impact. The end of the world.
Shinji Ikari, the son of Gendo Ikari, NERV's Commander, is called back to Tokyo III to become the pilot of Evangelion Unit 01. Along with the pilot of Unit 00, the quiet and reserved Rei Ayanami, he tries to figure out why he of all people would be needed to pilot the Eva. Asuka Langley Shikinami, the pilot of Unit 02, is soon added to their ranks as well, but is nearly killed while performing a link test with the brand-new Unit 03, which had been possessed by an Angel and had to be forcibly destroyed by Unit 01. The pilot of Unit 05, Mari Illustrious Makinami is also introduced, having slain an Angel that had been captured by another NERV facility and escaped.