Mitochondrial Transmortem Mutagenesis is the condition that creates "zombies" in the universe of George A. Romero's Night of the Living Dead and subsequent films of the franchise. Within that universe, a radiation cloud engulfed the Earth and permanently altered human mitochondria in a way that causes the dead to reanimate and attack the living.
A few minutes after somatic death, the mitochondria undergo a rapid functional mutation that allows for photosynthesis. The altered organelles now absorb a wide spectrum of light encompassing both violet and ultraviolet wavelengths. The resultant biochemical energy produced from this process is able to adequately power the motor neurons and lower brain functions. As the body becomes self-sufficient on this energy, the respiratory and circulatory systems become vestigial, ending the body's dependence on oxygen.
In the process of tissue decay before reanimation, all higher brain functions are destroyed. This leaves only the cerebrum to govern behavior. That in turn creates very animalistic behavior. Necrosis of the hypothalamus produces a massive flood of neurotransmitters, enzymes, and hormones such as norepinephrine and dopamine. These effects, combined with the painful symptoms of body-wide tissue decay, induce a psychotic rage and persistent hunger.
Although the fundamental cognitive functions of zombies are non-existent, their residual natural human instincts causes them to disregard cold putrid flesh (similar to their own) as a food source. Likewise, they are instinctively attracted to warm healthy flesh. An augmented sense of smell caused by a neuronal protein cascade during the reanimation process enables them to easily distinguish the two. As a result, zombies do not attack each other.
The body-wide necrosis added with the cessation of immune system activity, leads to the body of a zombie being flooded with lethal bacteria. That makes the bodily fluids highly toxic. Exposure to a sufficient amount of their saliva for example, will kill a person in a matter of hours.
Massive trauma to the brain is the most effective method of 'truly' killing a zombie.