How to Progress Regular Push-ups for Strength Gains

Push-ups are one of the most popular bodyweight exercises out there. I have known about it ever since I was a child. Push-ups are one of the basic exercises that people in the military does. Push-ups are the exercise that I did when I started Bodyweight training. It is a Beginner level exercises which work your chest, shoulders, triceps, and core.
If you are not a beginner and can do a lot of push-ups, regular push-ups are not going to benefit you. A lot of people add weights to their back while doing push-ups to increases difficulty, but you can change the technique of doing pushups and still make progress.

Shifting your weight to your weight to one arm increases the tension on to that part of the muscle and makes push-ups difficult. You can start to shift your bodyweight by doing assisted one arm push-ups or archer push-ups.
While doing assisted one arm push-ups, push your body with one arm and assist with the other arm. You can use a ball or chair to support your other arm.
If shifting your weight is difficult for you, you can first do it on an inclined plane and then advance to harder movements. Doing push-ups on an inclined plane is a good way to decrease the intensity of exercise.

You can make exercises more challenging by changing the tempo. Tempo is the speed at which you are doing the exercises. Usually, we do push-ups by going up and down with one second. Next time while doing push-ups, take 5 seconds during the eccentric contraction, it will be a lot harder.
By taking more time to do the exercise, you are increasing the time under tension and thus increasing the difficulty of the exercises.
Eccentric part of an exercise is when the working muscle lengthens, Concentric part is when the muscle is contracting, and isometric is when the muscle is when the muscle is neither lengthening nor contracting.
You can change the tempo of any of these parts to make it more challenging.
Reducing the time can also be challenging. While doing push-ups, you can explode up very quickly. Clap push-ups is an example for this.

By challenging your stability, you can add more challenge to push-ups. There are so many ways you can do it. You can add a lot of intensity by doing push-ups on a ball. Doing push-ups on an unstable plane forces your body to recruit more muscle fibers. Not only you will gain a lot more strength, but also great balance and stability.
Putting your feet to a wall is another great way to progress. When you put your feet on a wall, you need great stability and balance.

You can go deep while doing push-ups to increase the difficulty. Many of you should have heard this. When going deep, you are increasing the range of motion. More range of motion means, the muscle is more time under tension. Like in the previous point, instead of increasing the time, here we are increasing the range of motion to add more time under tension.
You can use books to elevate the plane and increase the range. You can also use small chairs. The trick is to add a more range to movement.
Make sure you don't go too deep than your maximum range, or else you will injure your shoulders.

That is all my ways of progressing push-ups. A lot of people still believe going beyond a push-up is not possible, from my experience of doing bodyweight training, I can tell you that it is possible. If you believe you can progress your push-ups, you can progress. Changing your existing techniques is the best way to do this. You can combine the above methods and make push-ups a lot harder. For example, you can shift your weight to one limp and do it on a ball. The extra weight and need of stability will make a simple push-up to a hardcore exercise.