You could do the effects in Illustrator, but I recommend Photoshop which offers more options for manipulating the grunge artifacts. You could also create an image map where the text takes on the texture of the background, making the effect much more realistic than just applying transparency to some grunge font. Whichever application you choose usually depends on budget and time.
In Photoshop, look into creating a "Displacement Map", "Layer Mask", and applying different "Blending" options. Not sure what version you are using, but the key to creating the artwork is the illustion of texture and the embedded look of the text in the background stone or whatever. This is fringe type creative work that requires a few steps to accomplish and certainly cannot be covered in this type of forum. See if you can get your hands on a good Photoshop Effects book.
You may also use a rubber stamp effect, as described in this good old thread,
or look into one of these ways,
and you may combine it with a colour transition (possibly including transparency transition) across the (outlined) Type/text.