Airports usually close or slow down activities in fog conditions, e.g. this seems to be a significant problem in winter at Delhi airport.
Large commercial aircraft would be able to land with no visibility (more accurately with no Decision Altitude/Height). However, if using the ground ILS, the runway must offer a Category IIIc landing system. While Cat IIIa and Cat IIIb are common at large airports, there are no Cat IIIc runways in the world of commercial aviation.
The reason is landed aircraft wouldn't be able to safely leave the runway and taxi to the gate because taxiways are not equipped with features appropriate to no-visibility conditions.
On the other hand driverless cars now are experimented on public roads without specific equipment, including in fog, and driverless vehicles push back aircraft prior to taxiing:
In the long term airports with autonomous tugs on the whole taxi phase may be interesting as they allow savings by providing power supply while taxing, which in turn can decrease fuel needs and mechanical wear.
Is there a possibility such zero visibility landings could happen in the near future, because desirable for airlines and airports?