One morning, while running a knife blade around his eye socket for the purposes of exploration*, Sir Isaac Newton thought up his Third Law of Motion, which states that for every action, there is an equal and opposite reaction. This is the reason that we have muzzle brakes on firearms, artillery pieces, and tank guns.

This train of thought arrived courtesy of a Savage Model 11 Scout Rifle, a .308 that weighs close to 9 pounds with a scope on it. The rifle generates about 11 foot-pounds of recoil, which packs the wallop of a butterfly fart, or perhaps a punch from Miss Natalie Portman. Nonetheless, Savage has seen fit to equip the Model 11 with a muzzle brake.

It is of the clamshell variety, which means that it sends the gas straight back instead of out to the side. This makes it somewhat more efficient as a brake, but also increases the noise, which is pretty awful with any short-barreled rifle, and with any muzzle brake. It also sends powder gas up your nose, which you may enjoy.

If you weigh the advantages of a muzzle brake against the disadvantages, it can be pretty revealing.

On the plus side:

Muzzle brakes cut recoil. Some are much better at this than others.
In some rifles, muzzle brakes increase accuracy because they cut down on barrel vibration, or alter it.
Muzzle brakes can drastically reduce muzzle jump, enabling you to keep your sight picture from shot to shot.

On the minus side:
Muzzle brakes increase the weight, length, and expense of a rifle.
Muzzle brakes drastically increase the amount of blast that comes your way. Blast can be as distracting as recoil, or more so.
Because muzzle brakes increase barrel length, you have to shorten the barrel to keep the length manageable, which costs you velocity.
Muzzle brakes change the point of impact. If you have one that unscrews you’ll have to re-sight the gun whenever you install or remove it. Some brakes come with muzzle protectors of identical weight that theoretically will let you keep your zero. Theoretically.

If you shoot without hearing protection you’ll go deaf. If you shoot with a muzzle brake and no hearing protection you’ll go deaf quickly.

In some circumstances, if you show up with a muzzle brake you will be asked to remove it, or leave.

Of course, there are some rifles that kick so hard you have to have one. The .50 BMG is one. So is the .338 Lapua and the .416 and .460 Weatherby.
As for putting a muzzle brake on a .308? Gimme a break.

*Sir Isaac Newton, in addition to being one of the towering mathematical geniuses of all times, was a very odd duck. He actually did run a knife point around his eye socket, and he would sometimes wake up in the morning, sit on the edge of his bed, get an idea, and become so engrossed in thought that he would sit there for hours without budging.