the top is usually grafted onto a hardier root stock. notice that the top leaves are different from the trunk leaves. I suspect the graft union got compromised and parts of the top died. This can happen when disease, insects or water enters a crack or damage in the union. Water can freeze during winter making a larger gap. Liken it to a wound being opened. I can see there's still some life left at the top but I can see that most of it has died. It's up to you whether you would like to replace the plant all together or just remove the dead branches and hope the remaining ones can grow big enough to fill in the spaces again.

Thanks so much for your response!

I didn't know how grafting worked. No wonder it looks like a different tree is growing out of the trunk! We also have a big ant problem in our garden and I know there was lots of ants at the base of this tree one summer.

I am going to have to replace the tree as I don't think the remaining branches will be able to fill in. This tree has not grown that nice since the beginning.

My other euonymus standard is doing better, but how come it doesn't grow into a fuller ball shape like I've seen in other gardens? (see picture) Do I need to prune it?

It may well have been the ants that made the grafted portion separate from the trunk.

Well regarding the other plant. All it needs is a good pruning to bring it to shape. Topiaries have to be maintained with good pruning to keep them in a rounded shape. Each time the branches are cut, the plant produces more leaves. Right now it's putting all it's energies towards all the overending branches.

Take this picture of yours, print it, with a marker draw a circle 1/3 from the bottom of the crown. Prune all branches that fall outside of the circle. I would suggest you do the same with the boxwoods below. These plants benefit from a good pruning. But in this heat, water well an hour before pruning.

Thanks for the tips!