A little over 70 years ago, the blade was claimed by House Keller, a rival house of the Blackgards. After the Kellers were destroyed the blade has officially been the property of Lord Trevyr Blackgard. As of recently, the blade has come into the possession of King Althurin I, the Black King of Ebonheart.
Blackest Heart is on display above the Ebony Throne in the Hall of Lords. Trevyr Blackgard briefly explains that the sword was passed down to generations of Blackgards through the centuries. He also notes that the blade hasn't seen battle for over ten years, as Trevyr last used it during the Greyjoy Rebellion.
After Eddin Blackgard is killed by his nephew, Steffon Blackgard, he claims the sword for himself. Steffon, now renamed King Althurin, later proclaims that he will claim the blade as his personal weapon, using it as a "sword for kings".
In the books
In the A Song of Ice and Fire novels, Blackest Heart is a huge and impressive weapon forged out of Valyrian steel and has been in the family's possession for over eight thousand years. Eddin describes the blade as taller than himself and as "gleaming like a thousand stars." As a Valyrian-forged weapon, it never needs sharpening. Its blade has a shiny and silvery appearance. For most of House Blackgard's history, Blackest Heart has been on display in the Hall of Lords and was rarely used for battle.
At this point in the novels, Trevyr Blackgard is still alive, and the sword is still hanging on its usual place above the Ebony Throne.