Personally I see Muspell, or more accurately Muspellheim, as a place, region, or world, and not as a Giant. If there was a Fire - Giant named Muspell he died long before the age spoken of in the Eddas, much as Ymir died long before the Golden Age. This fiery region known to us as Muspellheim is ruled over by a Fire - Giant called Surt, Surtur, or Surtr. Spelling does bot seem to have been all that important to the ancients as many of the Gods and Jotuns seem to have their names spelled differently by various sources. Surt, my preference, stations himself on the frontier border of Muspellheim, and guards it against all intruders. Surt has a sword of flames that is brighter than the Sun, and has the ability to light whole worlds on fire. Some, like Henry Adams Bellows, interprets one of the Eddas poems to mean that Surt has a female companion named Sinmara. According to Viktor Rydberg, however, Sinmara is the wife of Mimir. It is entirely possible that their are two females named Sinmara, and that this is the reason for the confusion.
Surt is of course best known for his role in Ragnarok. In the Lay of Vafthrudnir, Vafthrudnir asks Odin, who of course is in disguise, " What is the plain called where battle will be met by Surt, and the sweet Gods. " Odin answers that the pre - determined field is called Vigrithr, " Which stretches 100 leagues in every direction. " "Surt travels from the south with the enemy of twigs, ( also translated as : "Scathe of branches". Each author has a slightly different interpretation of the translation ) , the Sun shines from the swords of the carrion Gods. " In Gylfaginning it also says : " In all this great upheavel the sky will open up and through this will ride the sons of Muspell. " It is here on the plain called Vigrithr that Surt battles with Freyr during Ragnarok. Freyr is at a disadvantage because he gave away his sword while he was courting Gerd, and is subsequently killed by Surt in an epic battle.
After killing Freyr, Surt flings fire over the earth and the heavens, and burns everything . Surt's name has actually been deciphered by some to mean black, and some believe that that is his color because he has become charrred by his own heat.
The one thing that is not told to us in the Eddas is whether the hatred and animosity still exists between the " sweet Gods", and the Fire - Gods of Muspellheim in the future, when Asgard is ruled over by the son's of Odin and Thor. Surt is not killed in the final battle, and we can assume that he returns to his fiery homeland, but will the Jotun - Fire King still harbor ill will towards Balder, and the sons of the Gods. I guess that is yet to be seen, or written.
Although Surt is believed to be one of the more ancient figures in the Eddas, he may have been worshipped long ago as a Fire - Giant, much as Logi is thought of as the elemental form of fire itself. His name even lives on in modern times. In 1963 a Volcano erupted off of the coast of Iceland, and formed a small island. The island was quickly named Surtsey by the Icelanders. Also there is a moon that circles Saturn that is called Surtur, and there is a volcano on Jupiter's moon, Io, called Surtur. The name of Surt will forever be connected in our hearts, and our minds, to not only fire and destruction, but also for the warmth that allowed life to form in Ginnungagap, when the " heat met the frost of Niflheim ". For most of us, however, the name Surt will be synonomous with the end of the worlds and Ragnarok .
Go with Odin's wisdom, Freyja's love, and Thor's protection !