(a.k.a. Catalpa sphinx larva)
Some catalpa hornworms are black with yellow markings, while others look yellow with black markings. Both have a prominent, harmless horn at the tail end. There may be tremendous variation in size and appearance. The full-grown length is almost 3 inches.
There are 1 or 2 generations per summer but the large caterpillars in late summer are the only ones generally noticed.
The damage, even near-complete defoliation, is of relatively minor significance to the trees. Trees withstand the infrequent defoliation without lasting harm. Buds are not hurt and trees re-leaf the following spring as if nothing happened. This caterpillar is more annoying than damaging. The full-grown caterpillars crawl from the tree and cover the sidewalk, patio, etc. and annoy (but without really hurting anything). Fecal pellets are an unpleasant nuisance. Try to think of them as free "fertilizer."
A parasitic wasp attacks the caterpillars when they are numerous. The parasites live inside the caterpillar for several weeks and then emerge to form white cocoons that protrude from the back of the caterpillar.
Spraying is not advised, especially late in the season. If most of the caterpillars have reached full size it does more harm than good to spray. The trees withstand the defoliation, the insecticides are destructive to parasites and other beneficial insects, the caterpillars are difficult to kill and the damage to the tree has already occurred.