Depending on where you live it might be some sort of Hawk Moth or a Fawn Sphinx. If you want to search for the Sphinx better enter "Sphinx kalmiae" otherwise most hits will be for the cat Sphinx. .
Lime Hawk-moth Mimas tiliae
The blue horned sperm worm
A caterpillar that is pink and as a blue horn and found in France is called a hawk moth. These moths can grow very large.
Not a Hawkmoth, this is a swallowtail butterfly caterpillar.
The blue stripe caterpillar is commonly known as the "Hickory Horned Devil," which is the larval stage of the Regal Moth (Citheronia regalis). This striking caterpillar features bright blue and green coloration with distinctive horn-like projections. It is primarily found in the eastern United States and is often associated with hickory and walnut trees, which are its preferred host plants.
small and some can be green or blue or any color.
A horn worm either tomato or tobacco grows into a moth.
Lime Hawk moth catty
it is a Lime Hawk Moth originating from England
The name of the lime green caterpillar with an orange head is the cecropia moth caterpillar. The entire body is lime green except for a few small parts on the head which are a bright orange color.
green prickly caterpillar
The caterpillar that is black with a lime green jacket is the Saddleback Caterpillar. These caterpillars can sting and it will be very painful.