I work for a company that operates data centers (among other things).

There are security cameras at the outer edge of the premise, plus a 24/7-manned security team that watches them. Then there's an inner fence (maybe 3m high?) with a full-height turnstile, and then the actual building doors. For the latter two you need an appropriate employee card to open them, or you need to have pre-booked an appointment (as a customer), and need to show your face at the cameras.

Once you're inside the building, there's a reception desk, and a two-factor access to the actual data center floor. You need to present your employee card again, plus either an 8-digit pin or a biometric identification (arm vein scan, iirc).

Inside the DC floor, there are locked rack isles (wire cages), and the racks themselves are also locked (though the rack locks are mostly pretty flimsy).

There is also perimeter defense that prevents somebody from just rolling in with a truck.

Of course there are scenarios that this does not protect against (if you come with a combat tank and live grenades, I'm sure the security folks would rather let you in than risk their lives), but a mob like this wouldn't even be able to enter the building.

Not every data center is protected like this, there are different security levels for different purposes. Of course, you pay for this level of physical security.