28 Days Later and Return Of The Living Dead have both been cited as the start of the fast zombie genre, but 1980's Nightmare City got there first. Nightmare City is the first real fast zombie movie and came many years before the likes of 28 Days Later.
The series features Woody Harrelson, Jesse Eisenberg, Emma Stone, and Abigail Breslin as survivors of a zombie apocalypse. Two films have been released in the series thus far: the original film of the same name in 2009, and a sequel Zombieland: Double Tap in 2024.