Second Earth-Mars War

The Second Earth-Mars War is the main setting of ALDNOAH.ZERO. It was the second major conflict fought between forces of United Earth and the Vers Empire. It began in July 2014 and concluded in 2016.

Buildup
The reason behind the war 15 years earlier was because Vers being an impoverished, shabby country looked with scorn and jealousy upon Earth, a world with a vast history. The Royal family used the people's jealousy of Earth to maintain order on Vers and whipped the Orbital Knights into a frenzy and sent them against Earth, an action which alone caused the conflict spurring Heavens Fall. Count Saazbaum was sent to Earth as a scout, and his betrothed Viscountess Orlane later lost her life. He blamed the Vers Royal family for this and sought vengeance by making them pay with their own flesh and blood.

Operation Earthfall
In July 2014, after waiting 15 years since the end of the First Earth-Mars War that started with Heavens Fall, the presumed death of Princess Asseylum Vers Allusia during her goodwill visit to Earth gave the Orbital Knights a pretext to again, wage war with Earth.

Shinawara
In Shinawara, where Princess Asseylum was apparently assassinated, Sir Trillram tried to neutralize the assassins with his Nilokeras to prevent the knowledge that the Orbital Knights ordered the assassination from getting out. The daughter of the leader, Rayet Areash managed to escape and so Trillram pursued her as she sought refuge with the Shinawara High School students and the United Forces of Earth.

Tanegashima
As the Wadatsumi made its way to UFE headquarters, it stopped at Tanegashima, a former battlefield of the First Earth-Mars War, where she came under attack by the Hellas piloted by Countess Femieanne. The crew discovered the Deucalion, an abandoned ship.

Novosibirsk
By December, the Deucalion had reached UFE HQ in Novosibirsk, Siberia and the civilians were brought into the underground shelter. As Count Saazbaum now knew that the Princess was alive, he decided to launch a full-out assault on the military base.

Satellite Belt
A battle between Trident Base and Marineros Base.

New Orleans
Long after deployment in New Orleans, the UFE launches an attack on a Martian Knight whose Kataphrakt can fire powerful lasers, preventing UFE troops from being able to get within firing range. While UFE troops distract the Kataphrakt, Inaho uses his cybernetic eye to direct artillery fire for the Deucalion's main cannons from atop a vantage point. Since the Deucalion uses conventional artillery shells, it can arc its shots over the curvature of the Earth, protecting it from reprisal from the Kataphrakt (since lasers can only travel in straight lines). Eventually, the Deucalion manages to score a direct hit on the Kataphrakt, which causes it to explode, killing its pilot and he and the Solis are finally taken down by the UFE

Attack on Deucalion
Yacoym goes after the Deucalion's loading dock. While doing so, Harbinger Platoon engages him. The leader and two other pilots are frozen in their KG-7 Areion's. Inko Amifumi and Rayet Areash try to hold him off, and defeat him. However, they are unable to, and in the nick of time Inaho Kaizuka arrives. He engages the Elysium bit by bit firing bullets then grenades to temporarily create air bursts. This lets him get up right in front of the Elysium, allowing him to fire at point-blank range, destroying it

Operation Luna Gate
Operation Luna Gate was the final battle against Vers. While the Deucalion and main forces attacked the Moon Base's defenses, a covert mission a squadron from the Special Forces attempted to assassinate Asseylum, who managed to escape to Mazuurek's castle for safety with the help of Cruhteo's son Klancain.

Slaine and Inaho have their final battle, ending with Inaho defeating Slaine. Meanwhile, the other Vers nobles would engage the UFE forces and make their final attempt on the Deucalion.

Aftermath
After an unmentioned time in the future, it looks like peace is once again achieved. To strengthen the bond between the two planets(both Earth and Mars), an Aldnoah Reactor is created to give Aldnoah activation power to everyone on the planet, and the Vers Empire would be the ones to export the Aldnoah power to Earth and more capital for Vers Empire. Various scenes are shown depicting the lives of the characters after the war. It is mentioned that Slaine was killed, and that he was the one who planned Asseylum's assassination. (This is a scapegoat on Slaine). Empress Asseylum Vers Allusia, wishing for peace awakens the Reactor.

Inaho, now wearing an eye patch over his now removed artificial left eye, is shown visiting Slaine in prison. Slaine asks why he saved him; Inaho answers that he did it, because the Princess asked him a favor, to save Slaine. Slaine, becoming emotional from the realization that she still cared about him, cries. Inaho leaves the prison with his sister Yuki driving the jeep away. Asseylum is seen talking with Klancain on a battleship, saying that her time spent with Inaho on Earth are "lovely memories

Trivia

 * The picture shown above is from Episode 9 (Darkness Visible) which is before the crew of the Deucalion arrived in Novosibirsk. However, the landing of Saazbaum's castle is already seen, before it did so in the anime.