Rough breakdown:
Cabal Red Legion led by Dominus Ghaul showed up, destroyed the Tower and tried to steal the Light from the Traveler. It worked, temporarily. Our Guardian gets their light back and we defeat Ghaul. The Traveler wakes up. The burst of Light travels across the solar system and beyond and wakes up a fleet of Pyramid Ships.

We go into the Infinite Forest and defeat Panoptes, a Vex Mind.

We wake up Rasputin on Mars and defeat Nokris (Oryx's excommunicated son) and Xol, a Hive Worm God. (Though there is speculation that it's not actually entirely dead. Hive magic and what not)

Forsaken: Cayde-6 dies by the hand of Uldren Sov and his Scorn Barons. We hunt them down, and defeat them one-by-one, including Uldren. He's awakened later by a Ghost. We interact with his sister, Mara Sov, Queen of the Awoken and defeat Riven, the last remaining Ahamkara. This casts a curse upon the Dreaming City (Awoken homeland) that increases over the course of 3 weeks and then resets.

Shadowkeep: Eris Morn discovers a slumbering Pyramid on the Moon, hidden all this time. It's causing Nightmares, or apparitions of former evils to torture and taunt her and us. Simultaneously, the Vex invade the Moon via warp gates after the Gate Lord in the Black Garden is defeated.