The grip in the press and the bench press is commonly taken incorrectly.
Most frequently, the hand is place on the bar with the fingers perpendicular to the bar, then the thumb wraps under the bar, and the fingers wrap over the bar.
This however, will produce a bent wrist under a heavy load. The loads that you should be pressing as you get stronger will be too heavy to prevent the wrist from bending. This will cause the bar hand - and by extension, bar - to be unstable which will, in turn, cause failed reps. The possibility for wrist injury is also present.
In the initial pictures, you’ll see this common grip, and the resultant grip under load - you can clearly see how the load would cause bending on the wrist as shown.
There is a better way. Put the butt of your hands against the bar, and then turn your hands toward each other until your thumb is under the bar. Then let your fingers and thumb loosely wrap around the bar. Finish the grip by actually gripping the bar. You should loosely wrap your fingers initially, because if you consciously think “time to grab the bar” and try to do that, you will move your hands out of the correct position in an attempt to get your fingers where you think they should go. For the most part, you can forget about where you fingers need to be, as long as the other criteria are fulfilled.
In the below pictures, you’ll see the grip progression and appearance under load. The depth dimension adds some distortion to loaded-grip picture, but the bar is obviously loaded directly through the forearm (axially) instead of at a distance from it (moment arm).
This will create an extremely stable grip, because the bar is no longer loading the wrist with a moment arm. Instead, the force is axial to the forearm which will not produce bending on the wrist. This also makes it so that the load can no longer “bounce” the wrist up and down when you try to press the bar upward. This is the right way to grip the bar in what is called a “compression grip” - where the load is pushing into the forearm as in the bench press and press. The deadlift and chin up are tension grips, where the load is trying to pull itself out of your hands.
Just a heads up. It doesn’t feel right. It will feel more stable, but it will be awkward and weird. Try it a few times. Get used to it and you’ll never go back to the old, unstable way to gripping the bar like this.