I absolutely believe in reparations to specific victims. People often point to reparations for japanese americans who were interned during WWII as a precedent for reparations for slavery. The difference is that for the japanese americans, money was given to specific victims. If you do something unlawful to a person, they deserve compensation, but that only applies to the specific person.
Retroactive reparations are an awful idea though. If we gave reparations for slavery, the legal precedent would set off a massive chain reaction. Everyone whose ancestors had at some point been repressed would be entitled to compensation. If I could point to an Irish ancestry, I could claim that my ancestors that came to America to escape the Irish potatoe famine were wronged. I think the prolific "No Irish Need Apply" signs on buisnesses at the time make a strong case for injustice. Reparations for blacks, native americans, and other wronged minority groups would be disastrous, and accomplish absolutely nothing.
One branch of my family is composed almost entirely of White Southerners from Mississippi, some of whom did fight for the Confederacy. Therefore, I owe reparations to descendants of former slaves.
Another, smaller branch, of my family, is Cherokee. I therefore am owed reparations from Andrew Jackson's estate.
A third branch of my family is Dutch, and I am therefore in the midst of arbitration with King Juan Carlos I of Spain to pay me back damages for the harm done to my ancestors during the War for Dutch Indpendence.