Question: why is the overhead press like running?
Answer: because it's a great way to build strong muscles and healthy joints, in a functionally applicable way that involves a naturalistic movement and gives a lot of 'bang for your buck.' Or, it's a great way to wreck your joints and give yourself a pile of chronic injuries.

The same things that make the press great make it dangerous too. It tests a lot of attributes - so it develops them. Unless it exceeds them, whereupon you get injured. It works a lot of body structures - so lots of opportunities for improvement. Or injury.
Mobility is more important for the press than most people realize. Without the ability to extend the thoracic spine and shrug the shoulder up into the ear you're going to get hurt pressing overhead. Here's how to fix that:
Wall presses (front): stand facing a wall with a broomstick ready to be pressed. Touch your toes to the wall and press. Go slow and careful, and watch the bar path. You should finish with your elbows locked, shoulders high, and core braced.
Wall presses (back): try the same move but with your back against the wall. Touch the back of your head, your butt and your heels to the wall, then press and watch what happens.Are your knuckles touching the wall when you finish? If they are, but your butt isn't, you need to work on thoracic mobility (or lumbar stability).
Hindu Push-up: this means going from downward dog to scorpion poses in yoga, then pulling back to downward dog and repeating. Look it up on YouTube and see for yourself. It's good for building mobility in the shoulder.
Face Pulls: You'll want cables or a band for this. Think of it as an inverse row where you're pulling toward your temples instead of your chest. It's good for waking up and strengthening the muscles of the upper back and lower neck, which stabilize your spine when you press.
Band resisted press (front): get your trusty broomstick and a light resistance band. Put the band round the broomstick, then round a bar at about shoulder height or a little over. Step backward, facing the bar, til there's some resistance from the band, and then press overhead as usual. Watch the bar path and think about where your upper back and the points of your shoulders are.
Band resisted press (back): repeat the steps above, this time facing away from the bar. Keep your core tight and allow some stretching of the front of your upper body - let the band pull you into a more extended posture.
You'll also need impressive stability. If your bar is moving fine and your shoulders are doing what they should, but your core is slack, your lumbar spine is lordotic and your hips are doing the funky chicken, it's only a matter of time.
Additionally, try a half kneeling overhead press.
See Also: No Weights? No Worries!
Half kneeling overhead press: Set a bar up in a squat cage where your shoulders will be if you kneel up, with your thighs vertical. Kneel under the bar, kneel up and press from here. It puts more stress on the core and forces you to adopt better posture. Use a light weight.
Pressing Requires More Than Stability And Mobility
Pressing doesn't just require stability and mobility. If you associate those words with BOSU balls and reach for something heavy when you hear them, relax: your time has come. Pressing well builds strength: but you need some strength to press at all. Get a solid foundation and the press will reward you in everything from lifting to throwing. Skip ahead and you'll find yourself lifting your wallet and throwing some money to a physiotherapist.

Incline Presses: Set up a bench with as sharp an incline as you can cope with. If you're used to bench pressing, try starting at 45° and moving more upright over time. Press with a barbell if you can, though dumbbells are useful too. This should allow you to approach an overhead press slowly while retaining load and still getting a strength workout even as you move toward the new movement.
Landmine press: This is also known as the standing bar press. You'll set up a barbell with weights at one end, and the other end in a corner. If you don't want to wreck the corner wrap a towel round the end of the barbell. Start with the weighted end of the barbel level with where you'd rack the bar for overhead pressing, then press overhead. You'll typically start with the bar on one side and switch sides. Landmine presses allow you to use weight and get a feel for the overhead press, mirroring the stresses and strains on the whole body, which doesn't really happen with the incline press, but without the true overhead press' technical demands.
What about if you already press pretty well, and you want to improve?
You could try the SOTS press.
SOTS presses come to us from the world of Olympic weightlifting, where they're also known as 'press in snatches' and are often used as a prep exercise for snatching. But we're going to do them slightly differently.
You might want to start with a pair of dumbbells. Front squat, with the dumbbells held in the rack position. Then, in the bottom position of the front squat, press them overhead. When you're doing this for 3-5 solid reps with dumbbells, move on to doing it with an empty bar or a broomstick, and aim for a light bar at the end of 6 weeks. Then, see what it's done for your overhead pressing!
Some people can crank out perfect military presses on a daily basis. Others can't do the movement, whatever the load, more than once or twice a week without complaints from their joints. And some of us have a shoulder structure that means it's never going to be safe to overhead press. If that's you, don't worry about it. Landmine presses and incline presses can largely replace the overhead press in terms of outcomes without building up a backlog of nagging pain, tightness and dysfunction - but sadly, also without the satisfaction!
See Also: Weightlifting: Lift Slow Or Lift Fast, That Is The Question Now
If you found something here useful, or you'd like to take me to task on a mistake, please get in touch with me in the comments section below.
- Photo courtesy of Greg Westfall. by Flickr: www.flickr.com/photos/imagesbywestfall/3890281501
- Photo courtesy of ShawnHenning by Flickr: www.flickr.com/photos/shawnhenning/3329412991