The web is a spider web, and no cause for alarm.  Spiders are predators and beneficial because they eat many pest insects.  We are in a bad drought, and when there is little rainfall, spider webs seem to accumulate because the rain that normally knocks them down hasn't come for so long. Just be patient. No action needed. 

The leaves are very stippled (the white dots) by spider mites, which suck the juices out of the leaves.  Though your boxwood doesn't look very good because of that, it should put out plenty of new growth next spring which will mask it.  Again, no action needed.  

 However, we would recommend watering them deeply unless we begin getting a lot of rain.  Never allow your evergreens to go into winter in dry soil.  It can be very damaging. 

 Ellen

I am familiar with spider mites; I don't believe they are spider mites, even though the leaves are stippled.

Did you see the little white caterpiller-like insects?  Also, there is a central nesting place. I don't believe I've seen spider mites doing that.  The nest is also very dense in the middle.

Thx

Boxwood mites are specific to Buxus and are very tiny.
The thicker webbing is regular garden spider activity -a very old, holey web with a central funnel.
There are no caterpillars that are a problem on boxwood.
Here is our publication IPM:Boxwood: https://www.extension.umd.edu/sites/extension.umd.edu/files/_docs/programs/hgic/HGIC_Pubs/TreesandSh...


Christine