Hi, 

These appear to be boxwood. They are likely stressed and suffering from some other symptoms due to site conditions. 

The white stippling marks on the leaves look like Boxwood mite damage. It appears to be fairly severe so you may want to consider using an insecticidal soap or one of the other treatment methods listed to get ahead of it. The boxwoods most likely attracted the mites due to stress. Using the pesticide won't reverse the damage on the leaves, but you will be able to see if the new growth that emerges ends up with stippling damage and eventually as they grow it will cover the damaged leaves. 

We may also be seeing some dieback and bronzing from Volutella Blight which is a common fungal pathogen that is also a factor of stressed plants (stressed plants are more susceptible to disease and insect damage). You can try to trim out the dead or broken branches to help increase air flow to the plant. Make sure they aren't planted too deeply with the edging and mulch around them. Boxwood are fairly shallow rooted plants but just make sure the mulch or soil isn't piled up along the base of the plant where the stem meets the ground. You can also be sure to feel the soil in times of drought and irrigate as needed - the shallow roots can cause drought stress easily.  

Hold off on any fertilizer since that can just stress them further at this point. 

You can also read our Boxwood diagnostic page to be on the look out for any other problems. 

Let us know if you have further questions. 

Emily

Thank you so much for this incredibly helpful answer. Wow, the mite damage is severe. I'll follow all of your advice asap. Thanks again!

you're welcome