Damocles Crusade
The Damocles Crusade (also known as the Damocles Gulf Crusade) was a major campaign against the Tau Empire by the Imperium of Man.
It began as a response to first contact between humanity and the Tau, during what the Tau called their Second Phase Expansion. The Tau's colonization efforts brought them across the Damocles Gulf, and they encountered human worlds on the other side. These frontier planets were easy to subvert, as they felt little attachment to the Imperium, and even when there were loyalist factions, they were in the minority.
the Imperium was not happy to be losing worlds to Tau rule, so they sent a Crusade to toss them out, and eventually crush them all the way back to their home. They were so serious about this Crusade that they printed a special edition of the Imperial Infantryman's Uplifting Primer just for Imperial Guard Regiments going to the Damocles Gulf. They were initially successful, but as the Tau brought more of their armies to the front, the Imperial advance slowed and eventually halted on the planet of Dal'yth Prime. This was mostly because the crusade had outrun its supply line by many years. You'd think the Imperium would know better than to do that by now. They aren't exactly inexperienced at war.
Mind you, Dal'yth was a sept-world of First Sphere, meaning it was heavily fortified and there was shitton of fire warriors and auxiliaries garrisoned on it. Imperial fleet sustained heavy casualities even when approaching planet, and while the managed to destroy o repel all Tau and Kroot spacecraft, literally every one battleship of crusade was damaged rendering fleet useless for anything but guarding Munitorum transport ships till the end of campaighn. Regardless, imperial forces sucessfuly made planetfall, and at first day they crushed garrison forces on their landing zones with relative ease. This was the only thing they got easy on Dalyth. As war progressed, imperial forces found themselves constantly harassed by Tau night raids, carpet bombed by thousands of Barracudas and Tigersharks, and ambushed by Kroot kindreds. Even with their overwhelming numbers and orbital bombardment support imperial forces was tied by maneuverable Tau forces and unable to move far away from landing zones due to supply lines was torn apart by stealth-teams. Thousands of Imperial Guardsmen clashed with Kroot and Fire Warriors, while Space Marines was engaged in firefights with Tau battlesuits. Imperial titans found themselves in the fights with Manta destroyers, which wasn't favorable engagements for them at all, considering most Titan weapons aren't suited against fast flying targets. And yet humans advanced against all odds. Then Tau brought in reinforcements, lead by now (in)famous commanders Shadowsun and Farsight, and imperial reinforcements got lost in Warp only to appear one hundred years later (ironically to help Tau destroy Gorgon hive fleet), and conflict went to stalemate. Stalemated because, now that the crusade's supply line was who-knows-how-many years away, the rest of the Tau military had arrived. Not enough to stop the Imperium, of course, but enough to slow them until their lack of supplies eventually removed everything but lasguns and swords from play.
The Imperium probably would have kept throwing regiments and Titans at the Damocles Gulf, but that was when Hive Fleet Behemoth showed up and they needed every ship and guardsman they had to repel the invasion of Macragge, so they negotiated a cease-fire with the Tau and withdrew. The Tau Empire, shaken by the show of force from a power they thought weak and distant, tried to reassure the people and regain their expansion's momentum by re-taking all the worlds they had lost to the Imperium, and later launched the Third Phase Expansion to take further advantage of the Imperium's retreat redeployment.