From Destinypedia, the Destiny wiki
The surface of the Moon appears to be shattered with immense fissures in the crust spewing a sickly yellow miasma, hinting at the utter destruction going on deep beneath the lunar surface.The Hive have been buried within the moon for centuries, growing stronger within its lifeless core where they have carved their kingdom. Since the end of the Battle of Twilight Gap, a consequent Fallen presence has been encountered there in the form of the House of Exile. And at some point there were Cabal present on the moon. 
During the Golden Age, the Moon served as an outpost for supporting humanity's colonies across the system. The remains of an Accelerator and Moonbase can be found, used to deliver supplies to the colonies. The moon once housed a thriving human colony of interconnected bases, but now only broken domes and scattered space suits half-buried in the lunar soil mark humanity's faded dominance.
After the Collapse, the Moon was occupied by the Hive lead by Crota, Son of Oryx seeking the Traveler and its Light-bearers. There they hollowed out its mantle and fortified into their lair known as the Hellmouth.
Rezyl Azzir made first contact with the Hive on the Moon before returning to warn the City of the threat they pose. After the Battle of Burning Lake, Guardians attempted to take back the Moon in a disastrous battle that resulted in thousands of Guardians slain by Crota. Exploration efforts were repulsed, reporting increased enemy activity, and even strange tectonic phenomenon. and the moon is currently classified as a Forbidden Zone, accessible only to the most experienced Guardians. The forces of the Hive have now fully infested Earth's satellite, and pieces of the surface have cracked and broken off into space. An iconic view of the looming Earth hangs in the skybox, but Guardians would be wise to keep their eyes closer to the ground. A massive fortress known as the Hellmouth gapes open where the Hive have begun their dig, and sprawling networks of caves and fortified strongpoints wait inside. On the surface of the Moon, forgotten treasure hide in the dust.
The recent discovery of the Hive's deployment of Hive seeders on Earth, launched from the Moon, has forced the Vanguard to rescind their decision to principally avoid Lunar territory. Fearing further incursion, the Vanguard have begun sanctioning strikes against key Hive personnel and assets.
The Dark Below
Following the discovery of the Black Garden, the hive god Crota, Son of Oryx began to reawaken. This was preceded by the reappearance of Eris Morn an agent of The Hidden and member of the First Crota Fireteam originally assumed to be deceased. Following the instructions of Eris, the guardians were able to destroy the crystal containing the Soul of Crota and prevent his reemergence in the material plane. This instigated the opportunity to directly enter the Hellmouth and begin Crota's End.
The Taken War
When Oryx and the Taken arrived in the system new activity began in the Hellmouth. The Guardian traveled into the Hellmouth once again to claim a piece of the crystal that held the Soul of Crota, only to find it an empty shell. Hoping to make use of the dead god's essence, the guardian infiltrated the death ceremony of Crota using cloaking technology stolen from Rasputin, narrowly escaping the throne world thanks to the powers of Eris Morn.
Months after the loss of their Archon and Site 6, the Splicers sought to regain their advantage but lacked the leadership to do it. In desperation, the Splicers proposed an alliance to the crew of the mercenary, Taniks, the Scarred. To cement their alliance, the Devil Splicers used SIVA to resurrect Taniks as Taniks Perfected. Though Taniks' mind was overtaken by SIVA, his leadership and ruthlessness remained, giving them the advantage they needed. Unfortunately, their efforts were discovered by Variks, the Loyal who relayed their plans to the Vanguard. The Guardians led a Strike on the Moon against the Splicers, Taniks' crew and the Hive who were harassing them. Despite their efforts and Taniks' new abilities, they failed. With Taniks dead again, the Splicers were left broken and leaderless once more.
Red War and beyond
During the Red Legion occupation of the city and Ghaul's capture of the Traveler, he spread his forces to all places in the system, the guardians on Luna lost their light. According to Vanguard reports "Hive populations remain low and grow ever lower thanks to the efforts of a small contingent of veteran guardians who have made their homes on Luna". During a patrol, a Guardian by the name of Fenchurch Everis found an unknown object lodged in the chest of a Thrall on Luna that caused hallucinations when picked up, described as sharp, dark and slippery. The arrival of the Drifter and Gambit has caused a reduced Guardian presence on the frontiers, according to the Praxic Warlock Aunor Mahal; "in the absence of light, even the Hellmouth on the moon is stirring".
Nineteen months after the Red War, Hive originating from the Hellmouth entered the Ascendant Realm and infiltrated the Leviathan, which had been exposed to the realm by Gahlran, the Sorrow-Bearer. The significance of this is unclear.
The Guardians ultimately return to Luna following the discovery of a new crimson-hued Hive fortress near the Hellmouth, the Scarlet Keep. Worse, Eris Morn returns bearing a discovery: a massive black pyramid structure beneath the Keep, tied directly to the Darkness itself. The Hive manage to harness a fraction of the Pyramids power, creating Nightmare phantoms that take on the forms of the Guardians greatest foes. The Guardians now work with Eris to combat the Hive, their Nightmare creations and unlock the secrets of the Pyramid. They continued to battle the Nightmares, along with the Hive, Fallen, Vex, Cabal, and Scorn that are present with them.
The Guardians' situation on the Moon soon grew complicated when the relic they acquired from the Pyramid began sending a signal to the Black Garden. A fireteam of Guardians then enter the Black Garden via a newly-discovered portal on the moon, destroying Consecrated Mind, Sol Inherent and Sanctified Mind, Sol Inherent. At the end of their journey, the fireteam discovers a statue identical to the one found aboard the Pyramid.
However, the Vex would not take this incursion into the Black Garden lightly. The destruction of the Sol Inherent minds prompt the Sol Divisive to resurrect the Undying Mind. In turn, the Undying Mind copied itself across thousands of timelines after learning from its precious encounters; causing the Vex to invade the Moon en masse in an effort to bar entry into the Black Garden.
After weeks of holding the Sol Divisive back, the Guardians follow Ikora's plan to use a beacon to pull one of the thousand copies of the Undying Mind from the timeways, giving them an opportunity to destroy the Axis Mind. The Guardian push forward against the latest Vex Offensive, breaching into the Black Garden once again and planting the beacon. As planned, the beacon draws a copy of the Undying Mind and after a perilous struggle, the Guardians succeed in destroying the Undying Mind. However, as thousands of copies of the Mind existed, the Guardians were forced to continually destroy the copies one-by-one using the same process. Eventually, every last copy of the Mind was destroyed. However, the absence of the Undying Mind would allow the Red Legion to fracture time on Mercury, and across the solar system.
The Hunt for the Wrathborn
A little under a year after the Vex were driven back, Savathûn herself was ex-communicated, prompting her sister, Xivu Arath, to attempt to take over the Hive, including the Hidden Swarm. The Hive God of War sent her emissary to the Moon to construct Cryptoliths in the Hall of Wisdom and Shrine of Oryx, as well as commune with the remaining daughters of Crota to lure the Hidden Swarm under Xivu's command. However, Osiris interrupted the meeting, killing much of the Swarm's noble brood. However, he was unable to beat the Celebrant, resulting in Sagira's death and the Warlock to pursue the Celebrant in a blind rage. Eventually, the Guardian themselves returned to the moon, drove the High Celebrant back to Ascendant Realm, and retrieve Osiris with the help of the resurrected Uldren Sov.
Even after the Hunt had concluded, the Hidden Swarm still operated on the Moon, under the leadership of Crota's sole remaining daughter.
List of appearances