Did you "hill" them? That is is did you pull soil up around the stems as they were growing? At a certain point the plants will begin to die down though it seems a little early for that yet. Blight may cause them to brown early.

pull some dirt or straw over them so they don't turn green from sunlight then after the plants die get ready to eat them or try some now if you want some baby potatoes
They can't be doing to bad if you can see potatoes

Remember that if the potato turns green, the green part of the potato is poisonous! Be sure to cut ALL of it off before cooking. There is no preparation that will negate the toxin. you must physically remove.

There are many varieties of potatoes, some mature early, some late. If your potato plants are blooming (or have already bloomed), than your dieback is fairly normal for that variety. otherwise, they're just stressed some. But as jonas says, they can't be doing all that bad if you see potatoes being produced.