The zombie as reimagined by George Romero in 1967 was a remarkably potent monster that seemed to reach the deepest levels of primal fear. Yet it was a remarkably limited monster. It wasn't intelligent and even romantic like a vampire or even a werewolf when not transformed; not coldly intelligent like an evil space alien, or able to crush cities like Godzilla. Within the short time span of a movie, everything that could be done with them was essentially done in the original Night of the Living Dead. You might change the location to a shopping mall or whatever, but the setup was always the same: a group of people were trapped somewhere and the zombies were trying, always relentlessly, to get at them. It didn't help that the numerous films that followed usually had miniscule budgets, poor writing and minimally talented actors.
Then The Walking Dead showed the way. With a TV series there was time to do more than be trapped in some building. You could develop characters, move around, show interaction between groups of survivors, open the whole thing up, and this is what the Walking Dead staff and actors have done with great success. It's still a bit limited. You can go into the primary group's relationships and dynamics and this can develop characters, but too much of this and it can turn into a soap opera of who's in love with who or whatever and lose its way. Or, you can introduce the possibilities of conflict with other groups or villainous leaders of groups which creates opportunities for action beyond zombie killing. A few people have complained that it is getting somewhat repetitious by the end of season five, but it is still a somewhat limited template. I don't think those fans would want a full season of peace and happiness which is about the only alternative.
The Walking Dead has tried both directions with maybe a bit too much soap opera in the first half of season two and maybe too long of a single villain arc in season three, but each time has pulled back and brought the show back on track. Mostly it explores human nature when the protected life we knew that allowed us to be ultra-nice people disappears and the world becomes a hostile and dangerous place where niceness doesn't suffice any more and we have to bring out the tougher, harsher side of ourselves.,
The show does this wonderfully well and this is where you start. Be forewarned that the show can be pretty ruthless about killing off major characters. But if the primary characters were always safe like in older TV fare, it wouldn't be very unsettling and would become a bore. Like any of the better series coming out of cable these days it can be addicting. ENJOY!