They have no special powers. They have minimal identity or personality. Up until 2002, when 28 Days Later and (I’m told) Resident Evil made them fleet of foot, they lumbered around. In most conceptions, they merely hunger for human flesh.
A single zombie is an easy target. A single shot to the brain kills it — permanently, for good this time — in George A. Romero’s world.
It is only their easy, efficient reproduction that gives them any power — the exponential way that four become eight become 16 become 32 become 64 etc. if each only munches on or infects one other person.

The Psychopathic Chicken (and Other Lessons of Evolution)