At what point should I not allow my child to view graphic or violent television?

I'm not sure if this is controversial or not but it was something I was curious about. I came home from the grocery store and my husband was watching The Walking Dead while my son played in the living room. It was a particularly gory scene and while my son wasn't really paying attention to the TV it still had me worried. When he was a newborn we would watch whatever because he couldn't understand the violence but at what age do they start to comprehend things like that? I'm definitely going to start being more careful but was curious as to what other parents thought.