What was Hephaestus' domain?
Hephaestus (Vulcan in the Roman form) was the Greek god of blacksmithing, craftsmanship and metallurgy. Thus, his domain was fire, smithing, and forge. According to the prevailing Greek myth as described in the Iliad and the Odyssey, Hephaestus' parents were Zeus and Hera. Hephaestus was lame (he had a deformed foot), so Hera (or Zeus, depending on the myth) threw him off Olympus.
Hephaestus later returned to Olympus (he is the only Olympian to have been exiled and yet been able to return later), and he crafted magical armor for most of the Olympian gods and goddesses, as well as their thrones. He also crafted armor for a few select mortals and demigods, including the armor Achilles wore in the Iliad.
Since his primary craft is blacksmithing, Hephaestus is usually symbolized by a blacksmith's tools: an anvil, hammer, and tongs.