The Mushroom War (also known as The Great Mushroom War) is the cause of the condition today of the Land of Ooo. Not much is known about this but in some episodes they are clues that might have happen. During the war it was full of nuclear weapons, grenades, guns and other weapons. Many humans were killed but other characters might have been mutated but it was not yet confirmed. It can be infered the Mushroom Bomb brought about the end of the war, also creating the Lich. This is further supported by the ruined pieces of modern technology scattered across the land, and the beginning of the opening theme (which briefly shows the remains of nuclear bombs and other weapons). Marceline and the Ice King (Simon Petrikov) are the only known characters to have survived the Mushroom War.
Hunson Abadeer, Marceline's dad, was seen in a flashback in Memory of a Memory, showing him and Marceline after the War but before the establishment of Ooo. This shows that he is, technically, a survivor to the War, but he may have been in the Nightosphere when the Mushroom Bomb was dropped. This can be further understood in I Remember You, when Simon says that they may be alone after the apocalypse. The last piece of evidence to this is that in the flashback during that episode, Hunson was no where to be seen and Marceline is seen crying mouthing "Daddy", so it can be implied that he abandoned her sometime after the Mushroom War.
In "Finn the Human", Farmworld Marceline states the Mushroom Bomb was dropped 1000 years ago. In the Farmworld timeline, Simon Petrikov froze the Bomb in midair, though it came so close to contact that it crushed him. Current Marceline is also 1000 years old. This means that in the normal Universe of Adventure Time the Bomb would have also been dropped around 1000 years prior to current events.
The first mention of the war in continuity was in "Video Makers" when Finn and Jake discover government copyright warnings before the movies they watch for their film club. Even though the civilizations that created these warnings would have been long gone by their time (and that films bought for home video usage generally are protected to be used for private usage only, which being held in a home would be considered as such), they decide to abide by them to avoid breaking the law.
Strangely, the Land of Ooo also contains technological devices that are far more advanced than what exists today, such as Universal Translators and holographic newspapers. It is unknown whether these are based on prewar technology (the year of the war was never stated, it could take place centuries after our time) or are more recent inventions.
In "I Remember You," the Ice King is shown to have a drawing of earth with a giant meteor headed towards it, possibly resulting in the missing chunk- although this may be referencing the asteroid in the episode Wizard.