Spartan Ops
Spartan ops is how the campaign of Halo 4 was continued. With its focus on Fire Team crimson, it follows the event that take place starting six months after the events at the end of Halo 4. You find your self on the planet Requiem, an artificial world made by the ancient and incredibly advanced race known as the Forerunners. In the campaign, you, the player, have learned that Requiem was where a member of the Forerunner race known as the Didact (or as he's known in the expanded universe, Shadow-of-Sundered-Star), who was placed in the core of the artificial world a hundred thousand years ago by his wife The Librarian after he used a device known as a Composer to turn a tribe of prehistoric human into robots called Prometheans, which were used to fight an alien parasite called The Flood. The Librarian hoped that the time he would spend imprisoned would change him. But that's beside the point. After the Didact is defeated by the Master Chief, the absolutely gigantic human star ship called the UNSC Infinity is sent to Requiem to learn more about the planet, and with its many fireteams of Spartans defeat any Covenant forces on the planet. There's a lot more to it then that, but a lot of that has nothing to do with Halo 4 or Spartan Ops in terms of game play. I might go into greater detail if I do a review or a play through of other games in the series.
Above: The Didact, the antagonist of Halo 4.
halo 3 ODST
Halo 3 ODST, or Halo ODST is a sequel/ expansion to the story of Halo 3, although due to what happens in the open cut scene, some would argue that it takes place during Halo 2. Unlike it predecessors Combat Evolved, Halo 2, and Halo 3, ODST has the you play as members of an squad of Orbital Drop Shock Troopers. You start out playing as Rookie (no name, just Rookie), who's drop pod lands in New Mombasa, where a portal made by the ancient race called the Forerunners to a structure that they made outside the galaxy called the Ark was buried. When the Prophet of Regret's ship jumped into Slipspace, it trashed part of the city and unearthed the Ark portal. A squad of ODSTs