The Darksaber has a long and fabled history that, for the most part, doesn't seem too confusing at first. It was created by the Mandalorian Jedi Tarre Vizsla, returned to the Jedi Temple after his death, and was later recovered by House Vizsla. It remains within the Vizsla clan until the Clone Wars when Maul takes it from Pre Vizsla, but here's where things get messy. Before this, Obi-Wan Kenobi (James Arnold Taylor) defeats Vizsla in combat before he calls his Mandalorian warriors in for backup. Shouldn't that mean that the weapon belongs to Kenobi? If this were the case, it would create an entirely new lineage that looks vastly different from the one we know.
Ignoring Kenobi's hypothetical reign and any that could've come after, Luke Skywalker's aforementioned claim isn't perfectly sound either. It can be argued that Vader's defeat of Sidious and subsequent demise puts the Darksaber in Luke's hands since he's his biological son, but the situation isn't that cut and dry. As Vader lifts Sidious and tosses him into the chasm of the Death Star II, his Force lightning severely damages Vader's suit, which leads to his death. Therefore, does that mean that their confrontation ends in a draw? If so, what would that mean for the Darksaber?
All in all, the Darksaber is a cool-looking weapon that's synonymous with some of the coolest looking "Star Wars" characters, the Mandalorians. It's just too bad that the history and rules surrounding it are a bit convoluted, to say the least.