Originally Posted by FlyerJosh

You can continue the approach if reported vis drops below minimums after you pass the FAF, but must discontinue it if drops below mins outside of the FAF. To land, you must have the required FLIGHT visibility (IE if you see the lights at decision height, you continue or you go missed). Doesn't matter what the tower/ATIS is reporting.

Remember too that in the 121 world, ONLY visibility is the limiting factor for flying the approach (IE if you have VV00 and 1/2SM, you can attempt a regular ILS, but if you have CLR and 1/4SM you can't fly the approach).

Of course these rules only apply to commerical ops (Part 91 can attempt the approach in 0/0)