Preface: I AM IN NO WAY A MARTIAL ARTS EXPERT. What follows are observations and assumptions based on the most common aspects of Zombology. Yes it's a word. Shut up.
Hand to hand, the choices seem limited. Zombies feel no pain, so pressure points, etc are useless. They can't be knocked out. A skull is one of the hardest bones to shatter. They don't need to breathe, so they can't be choked.
So what is left? Well they attack by grabbing and biting. Limited attack moves. They don't try and knock you down, they don't roundhouse you like Chuck Norris. Just grabbing and biting.
Get your hands off me you damn dirty ape!The first defensive move then, is to either block, or escape a grabbing attack. Once free, you can run.
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Sweep the leg...Do you have a problem with that?Zombies don't have great co-ordination, so you could try to throw or trip them.
[Captions to go here] A simple way to take a zombie down would be grab them by the throat and put one leg behind theirs and trip. While this could be risky if your fast enough to grab their throat that would keep them from biting you then just grab their arm and trip. Also for any wrestlers out there a simple hip throw could work as well if performed fast enough. Sorry if you don't wrestle but explaining the move would be a little too difficult, but you could ask someone who does wrestle to show you. One last thing. if you want to take a zombie down by grabbing the legs there is an easy way to do it quick. Put your right foot out (or left whatever you prefer) then press your head to their chest and pickup one leg and drive to the opposite side. Try not to follow them to the ground if you can help it. If you do then get up as fast as humanly possible. These may be risky but if you do them correctly they could get you out of a sticky situation.
Smile you son of a *****!If they can't bite you, they are less of a threat. So a broken jaw would be a good offensive target.

These are the five parts of a lower jaw. The two parts you are aiming for are the Green, White and Yellow sections. Black is the ramus, and is protected by thick layers of muscle. Red is the body of the jaw, and is the thickest part of the bone. Green is the parasymphysis, or chin. Usually this is broken either straight-on or from below. White is called the angle, it has the smallest surface area and so is the smallest target. The yellow section is the condyle. This connects the lower jaw to the skull. It is frequently broken by a blow to the side of the head.

This shows the section in more detail. The black arrow points to the condyle, the white to the coronid process. The process keeps the jaw in line as it moves up and down. Breaking it makes biting awkward, and painful, but still possible. The condyle is the pivot point for the jaw. This is the target.
When hitting the chin straight on, the head has room to go back. From underneath, the force of the blow can be transferred to the teeth, which can break and dissipate the power. But when hit properly, the condyle will bend, because the chin, body and angle of the jaw have a lot more lateral movement than the condyle. You are looking to make the bone flex and break, not pulverise it into dust. The red dot is the sweet spot.
Run, Forrest, Run!Preventing them from running after you or from grabbing you would be a good second best. Remember that since they don't feel pain, you are looking to break the limbs, something that requires both strength, and precision, since you need to aim for the either the joints or the centre of the bone. Joints are held together by muscle, tendon and cartilage, which will tear and break much more easily. Kneecaps are a favourite. Bones are fairly inflexible, but the point that flexes the most is equidistant from either end. Always go for the lower half of the limb. Radius and ulna break more easily than the humerus, and the tibia and fibula break more easily than the femur.

The ankle is another joint target, however since it is possible (but painful) to walk on a broken ankle, I doubt it will give Zack too much trouble.
I was eighteen months in the bush...Finally, you could try breaking the neck. Not recommended for amateurs. By doing this, you are severing the spinal cord, preventing any brain signals to the body. Whilst this might also kill the zombie, the goal is incapacitation to allow you to escape, or grab a weapon and finish it off.

No, I will not tell you how to perform this. There are way too many idiots who will go out and try it on a human. What I will tell you is WHY it kills people, but not necessarily zombies.
When most people think of a severed spinal cord, it's usually accompanied by some poor bastard in a chair. Alive, but paralysed. The neck snap you see in movies (and no, that's not how to do it, they don't want idiots copying it, same as me) kills because it severs the cord higher up in the spine. Up high enough and it will kill the signals that tell the heart to keep beating, the lungs to work. The reason you don't see a human head flapping its mouth in fear is beacuse they either go into shock and pass out with the brain waiting to die of oxygen starvation, or they suffer Sudden Nerve Trauma. WWZ says it's "like God flicking your life switch."
But if a zombie brain doesn't need oxygen, and doesn't suffer from SNT, would a neck snap kill it? Probably not. But it can't move below the neck, so walk away, grab a brick, crowbar, whatever, and do the job.
Can't we all just get along?Most people on this site are proponents of one martial art or another. Several threads talk about whether Krav Maga, Jujutsu or MCMAP are the best fighting style. But these are all fundamentally flawed, in that they are conceived and refined around the conecpt of one human fighting another human. Whilst zombies are physically humanoid, their physiology gives them core differences in technique and capacity for punishment.
For those who are skilled at any particular discipline, please feel free to update this page with moves and techniques that you think are beneficial. The goal of this page is to combine all the appropriate existing techniques, add new ones, and eventually define a style for dealing with the undead.
In World War Z, it is referred to as "Mkunga Lalem", which means The Eel and the Sword. I guess it's descriptive of escaping the grasp, then attacking. I am open to alternative names though, since this will be a ZSDW collaberation.
One of the fastest way to remove an opponent from a fight is to lock your ankle into an l and hook behind the opponents, about the position of the Achillies Tendon. As you do this you bend down and in one movement sweep the foot away while striking the center of the chest between the nipples with a palm heel strike. In doing so you knock the opponent backwards and spinning in the direction of your choice (sometimes you can actually take down two people at once) since at no point do you present yourself in bite range, this move would also be very effective against zombies. I would still reccomend light body armor however.