How do real life armies clear cities?

[Mustang]

At present, my main infantry-clearing tactic is to buy a bunch of jeeps and run them through the enemy defences until they get shot at and reveal the position of the enemy. Some people say that, if possible, you should take a heavy HEAT-proof tank (like the Abrams) through a city, but this is a bad idea for two reasons. One, it dosen't draw fire because the enemy isn't going to bother to shoot at it. Two, it can't spot infantry very well at all, and will often end up in a hex adjacent to an enemy infantry squad, not spot it, then get close assaulted the next turn. And three, they're just soo damn expensive that you can't loose a single one, and driving through close terrain you will eventually take some kind of flank shot from an RPG.

Of course, my current "suicide jeep" tactics aren't very realistic, because few actual soldiers would be willing to drive their vehicles into certain death. Does anyone here know what armies will usually do in a urban situation? An infantry-only advance, heavy artillery bombardments, a combination of those, or what?