How a local crew fixes it
The fix depends on the wall and on why it cracked.
Foam injection
For a leaking crack in a poured wall, foam is pumped in through small ports. It swells to fill the crack from the inside face to the outside face. It stays a little flexible, so it handles small seasonal movement. It is often the first choice when the goal is to stop water.
Epoxy injection
Epoxy is pumped in the same way, but it hardens like glue. It bonds the two sides of the crack back together. It is often used when the crack needs to carry load, not just stop water.
Bracing first, then sealing
If the wall has moved, sealing the crack alone will not hold. The wall needs to be braced first. That can mean carbon fiber straps, steel beams, or wall anchors. Then the crack is sealed. See wall anchors.
Block and stone walls
Hollow block and stone walls are not injected the same way as poured walls. Cracks in these walls are often fixed with new mortar, bracing, and an inside drain that takes the water away. See basement waterproofing.
Outside repair
Sometimes a crack is dug out and sealed from the outside. This costs more and tears up the yard. It can make sense when the outside wall needs work anyway.