Just to supplement the answer by /u/kookingpot

Archaeologically, most attention has fallen on "Troy VIh" and "Troy VIIa", the settlements of the 13th and 12th centuries BC. These are known mostly from excavations by Carl Blegen in the 1930s and Manfred Korfmann between the 1980s and 2000s.^1 Excavations in Troy VIh found a destruction with buildings and walls collapsed, but no sign of burning and no human remains.^2 Some bronze arrowheads were found.^3 Excavations in Troy VIIa uncovered evidence of a destruction layer including burning, some weapons in the form of bronze arrowheads and piles of slingstones, and skeletal remains in amongst destroyed buildings.^4 However it's worth pointing out that Korfmann's conclusions have been extremely controversial, and not everyone believes Troy VIIa was destroyed by war.^5 Even if it was, there is no indication of who the destroyers were.

Some possible archaeological correlates of the events detailed in the Hittite texts come in the form of a possible depiction of an Aegean warrior on a bowl from the Hittite capital of Hattusa (modern Boğazkale),^6 and an inscribed sword of possible Aegean type brought back to Hattusa as spoils.^7 Both date to the 14th century BC.

^1 See Blegen (1963) Troy and the Trojans; Studia Troica 1-19 (1990-2011).

^2 Hiller (1991) “Two Trojan Wars? On the Destructions of Troy VIh and VIIa”, Studia Troica 1; Mountjoy (1999) “The Destruction of Troia VIh”, Studia Troica 9.

^3 Blegen, et al. (1953) Troy III: The Sixth Settlement.

^4 Blegen et al. (1958) Troy IV: Settlements VIIa, VIIb and VIII; Korfmann (2002) "Ilios, ca. 1200 BC - Ilion, ca. 700 BC", in Omero, tremila anni dopo.

^5 Easton et al. (2002) “Troy in Recent Perspective” Anatolian Studies 52.

^6 Bittel (1976) “Tonschale mit Ritzzeichnung von Bogazkoy”, Revue archeologique 1.

^7 Cline (1996) “Aššuwa and the Achaeans: The ‘Mycenaean’ sword at Hattušas and its possible implications”, Annual of the British School at Athens 91.

I actually wrote an answer on a very similar question some time ago. Here's the thread, you should check it out because there are a couple other good answers besides mine as well. I'm going to copy an edited and slightly expanded version of my answer here:

There really was a Bronze Age conflict which probably inspired Homer's epic.

Did any of the people in the story exist? We have no evidence for that. Did events happen as described in the story? Probably not, it was probably very embellished (like historical fiction movies/books). But we know from Hittite archives that there was a conflict between the city of Wilusa (the Greek name for Troy is Ilion, which is a cognate/loan word from the Hittite name for the city, Wilusa) and a people group called the Ahhiyawa (often identified as the Achaeans). The specific text refers to something called "the Wilusa episode" which involved hostility on the part of the Ahhiyawa toward Wilusa, which took place around the 1300s-1200s BC. All ancient Hittite textual indications and current scholarly consensus is that the Ahhiyawa are from the area of Greece/Mycenae (very similar to Homer's Achaeans).

The identification of Wilusa as Troy is also pretty sound, historically and archaeologically. All textual references that locate the city geographically put it in the area that the mound of Hisarlik (which was identified as Troy by Schliemann) sits, and there are mentions of projects at Wilusa, such as a water tunne,l in Hittite texts, which have subsequently been found in excavation at Troy. So it's pretty well-accepted that Troy=Wilusa=Hisarlik.

So we know that there was a city called Troy, and a people called Achaeans, and that the Achaeans attacked the city of Troy. This has been corroborated in Hittite texts as well as by archaeological evidence. Lending further credence to the idea that the conflict actually happened is the fact that one of the kings of Wilusa mentioned in Hittite texts was Alaksandu, which is the Hittite version of Trojan prince Paris' birth name (Alexandros). This king is not considered to be identical to the character of Homer's story, but it serves to underline the fact that the names of characters were not at all out of place for the time, and his character could be based on an actual historical person.

Now, since we understand that there was in fact a conflict between Greeks and Trojans, how much credence can we put in Homer's account of it? The answer is not much.

Homer wrote his epic centuries after it took place, between 1102 BC (Pseudo-Herodotus' date) and around 850 BC (Herodotus' estimation). We have no indication that it was intended to be an accurate retelling of events, or anything more than a fun imagining based around something that actually happened (like Inglourious Basterds and WWII, or "Cold Mountain" and the Civil War). A historical fiction, if you will. Homer took a real conflict, and constructed a most likely fictional account centered around that real conflict. All we know is that yes, there was a war, and the Achaeans attacked Troy, and that's about it. We don't have any evidence for Odysseus, or Achilles, or a giant wooden horse, or any of that stuff. But the super broad strokes of Achaeans attacking a city called Troy do in fact appear to have taken place.

For further reading, I suggest

Sagona, A G, and Paul E. Zimansky. Ancient Turkey. London: Routledge, 2009

Easton, D.F.; Hawkins, J.D.; Sherratt, A.G.; Sherratt, E.S. (2002). "Troy in Recent Perspective". Anatolian Studies (52): 75–109

Allen, Susan (July 1995). "'Finding the Walls of Troy': Frank Calvert, Excavator". American Journal of Archaeology 99 (3): 379–407

Wood, Michael (1985). In Search of the Trojan War. BBC Books; First Thus edition