Seeds and tissue of the milkweed plant (Asclepias spp.). In captivity, the bugs feed on shelled sunflower seeds.
I'm trying to figure out the "in captivity" part. Do people keep these insects as pets? Do they house them for some sort of mad scientist experiments?
Whatever the case these insects eat the juices of various varieties of milkweeds which makes them pretty much unpalatable to any potential predators. This is very similar to monarch butterflies whose larvae also ingest milkweed. Depending on how much you like milkweed (and I don't know anyone who doesn't, maybe I just don't know enough people) these orange and black milkweed munchers aren't welcome inhabitants of the garden.
They are easy enough to pull off or knock off into a container for disposal so they aren't really a threat. They serve to help control the population of milkweed in the wild and while that may be necessary it's hard to look positively upon an insect that enjoys dining on my garden. Of course monarchs of all ages are welcome!
What insects are bugging you?