Doomsday vs Superman is a number of story arcs related to, well... Doomsday and Superman.
The Death of Superman
"The Death of Superman" is a comic book storyline (culminating in Superman #75 in 1993) that served as the catalyst for DC Comics' crossover event of 1993. The completed multi-issue story arc was given the title The Death and Return of Superman.
The storyline's premise is as simple as its title: Superman engages in battle with a seemingly unstoppable killing machine named Doomsday in the streets of Metropolis.
In the three issue mini-series Superman/Doomsday: Hunter/Prey (1994), Superman journeys to Apokolips and Calaton to find Doomsday's body. Assisted by Waverider, he confronts Darkseid and Hank Henshaw, and finds that his killer is still alive and discovers the details of Doomsday's origin. In Superman: The Doomsday War (1998), Doomsday's mind is under the influence of Brainiac and Superman fights two of his most powerful enemies, in order to rescue Lana Lang's newborn child.
Day of Doom
In the days before the anniversary of Superman's death, Ty Duffy, The Daily Planet's staff reporter, retraces Superman's cross-country battle with Doomsday; Duffy resents the assignment. During the investigation, a mysterious figure also follows Doomsday's cross-country path, and commits a series of murders along the way.
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The Death of Superman (1993)
Hunter Prey (1994)
Day of Doom (2003)
Miscellaneous (1995 - 2006)