holy balls. Tear that thing out. They may have used greenboard behind there. That shower is toast. There is mold everywhere, grout is coming out, the stone is saturated from behind. Don't touch it.
Edit: I spoke with Mike about this on the phone. It may not be as bad as my original post suggests. Mike thinks it may be a steam shower, which would make sense. it is common for marble and other stones to turn white in steams showers from the moisture accumulation on the walls leaving mineral deposit buildup. It bonds with the stone and would need to be cut off with diamonds if this is the case.
The mold is another story. That shower is in really bad shape. I would start by removing all the grout from the perimeters, anywhere that a vertical/horizontal surface meets, cleaning with MB-9 mold and mildew remover, then cleaning the grout and floor with acid (yes acid, in a limestone shower) to get everything cleaned up. Then diamond refinish and hone and/or polish, clean and polish the glass, then the last thing install new sanded grout, wait 24 hours then seal the shit out of it with a really good impregnator for porous stone.
this is a 3 day job. It REALLY helps to be able to switch off with a helper. If there is other stuff to do in the house, you guys can switch off. They most likely have countertops that need to be refinished. I can't believe people shower in that.