For a long time, not just the Trojan War but the city of Troy itself was held to be mythological. In the late nineteenth century, however, Heinrich Schliemann uncovered the ruins of a Bronze Age city that corresponds with many descriptions of where Troy must have been. Based on Mycenaean and Trojan archaeological evidence, historians and archaeologists believe that a series of conflicts did actually take place between Troy (in Asia Minor) and the Mycenaean cities (in Greece) in the Late Bronze Age (1400-1200 b.c.e.) While the causes of the conflict can only be speculated at, what is known is that the city of Troy suffered enormous destruction during this period, and was apparently burned to the ground. While we cannot know, the Iliad may refer to events in this conflict that attained legendary status over time, particularly as Mycenaean culture was destroyed by Dorian invasions that ended their Bronze Age heyday.
The Trojan War was in fact a real war, but the reasons that lay behind the war may be varying widely. It is however known for sure, that the story of the Greek Horse, is in fact a myth.
The Romans also consider themselves to be descendants of the Trojans, and more specifically, Aeneas. A trojan commander. The Romans must have had some basis for this story, as it couldnt have been completely made up.