One arm push up progressions from easy to difficult. Also lots of intense one arm push up variations.
One arm push up is a real strength builder that develops strength and size in the chest, shoulders and triceps. Your core also needs to work incredibly hard to stabilize the trunk (anti-rotation).
Once the basic push ups become easy, starting to work on one arm push ups is a great way to progressively increase the difficulty of your horizontal pressing exercises.
The biggest benefit of one arm push ups is that they can be done anywhere: at home, at the gym or outdoors. It's a fantastic option for people who prefer to train by using only their bodyweight and prefer to workout at home.
Below you see the best progressions from easy to difficult. The hardest ones are truly the hardest pressing exercises almost anyone can do.
You can do one arm push ups on your palm, fist, bar or on fingers. The fist increases the activation of the triceps (which is why it's a lot harder) and makes the exercise easier on the wrist.
Many will point out that the correct form is to tuck the elbow. It's definitely a good form, but it's not the only correct form.
When your elbow is flared (as in the rocky push up), you will use more of your chest muscles. When the elbow is tucked (inside), you will hit more the triceps and shoulders.
Flaring elbows is not "bad for your shoulders" (unless you have pre-existing shoulder problems and in this case most normal exercises would be bad for your shoulders).
Many people actually find flaring your elbow to be much easier for the shoulders than the "correct form" where your elbow is tucked.
People think flaring your elbow is bad for your shoulder, because most people consider the tucked elbow one arm push up the correct form. In reality all forms below are the correct ones - they just emphasize different parts of the body.
One Arm Push Up (OAP) Progressions
1. Incline OAP

Elevate the upper body by doing the one arm push up against a bench, a table, a wall or anything else. This way you are pressing less of your bodyweight which makes the 1 arm push up a lot easier.
2. Negative OAP
Take the one arm push up stance and lower yourself down slowly with control. The slower you can do the exercise, the better. When you touch the floor, press yourself up with both arms.
3. Rocky Push Up (Wide Legs)

Sylvester Stallone used to do wide legs explosive one arm push ups from side to side in Rocky 1. By widening your legs, you make it easier to stabilize the core and you will be pressing less of your total bodyweight (which makes it easier).
Your elbow can be flared which increases the activation of the chest. This also makes the exercise easier because the chest tends to be a very strong muscle for most people.
4. Head OAP

Place your hand next to your head by strongly flaring your elbow and turning your fingers inwards. This places your body in a mechanically advantageous position which makes the exercise surprisingly easy.
Contrary to popular belief, this is not bad for your shoulder unless you have pre-existing shoulder problems or you are way ahead of yourself in terms of what progression you should focus on.
5. One Arm Push Up (Elbow Tucked)

Keep your legs shoulder width apart or a bit wider and do a full one arm push up with your elbow tucked.
When your elbow is tucked, you primarily do the exercise with your triceps and anterior deltoids. It's also harder to stabilize the core and you are pressing a bigger percentage of your bodyweight, which makes the exercise a serious test for your fitness.
6. Lateral OAP

Lateral one arm push up is an intense variation of OAP where you are keeping your body sideways and pressing yourself up from the side.
Lateral push up focuses more on your triceps and shoulders, while you also need to work hard to stabilize the body.
7. Decline OAP

In the decline one arm push up you are elevating your legs which makes OAP significantly harder since you need to press more of your bodyweight with every repetition.
8. Single Leg OAP

Single leg OAP is an intense balancing act that also requires tons of strength from your pressing arm.
Your body not only needs to press your bodyweight up, but the engaged muscles (and many others) need to work incredibly hard to stabilize the body and manage anti-rotation.