There are many different types of fire mythology, some involving tales of how humans acquired fire and others relating to fire deities more generally. Fire is a very important part of most human civilizations, and so it is very common for mythological systems to have elaborate stories about the element. One common type of story involves a god or trickster giving fire to mankind, but others elaborate on the nature of fire itself. In addition to these stories, there are also many tales involving fire as a plot element or tool.
Some of the most common types of fire mythology involve fire deities who may or may not directly use fire in the story. Often, the god or goddess is merely associated with fire either because of his or her form or because of elements he or she is thought to rule. Kagutsuchi, for example, is a Japanese fire god who burned his mother to death when he was born, prompting his father to cut him into eight pieces. In these stories, the deity's association with fire may not play a central role in the plot, but members of the culture who are familiar with the mythology will understand that this god is associated with fire even if that fact is not mentioned specifically.
A very common type of fire mythology involves humans stealing or receiving fire from the gods or a forbidden land. Few stories involve humans creating fire themselves, with most relying on an original source of fire or source of the knowledge that makes fire. For example, the Prometheus myth concerns how a Titan stole fire from the Gods and gave it to mankind, which resulted in eternal punishment for Prometheus.
Many cultures have similar stories concerning heroes and other individuals who travel to the land where fire is located and take it back to mankind. Native American myths often have stories of this type. Tricksters like Coyote can also be responsible for stealing fire. In fire mythology of this type, the gods are often angered and punish the thief.
Some fire mythology examples do not fit precisely in either type. Fire can, for example, be personified. There is a myth in which Anansi the spider invited Fire, who is a character in the story, to dinner and burns Anansi's house down. Fire as a plot element is also often featured in myths because fire is a major part of human life. Characters might burn a sacrifice or appease the gods with fire or use fire in any number of other ways.