The basic premise of this fanfic is that Harry Potter is disguised and adopted into the Ancient and Most Noble Family of Black. This premise is executed in a very heartwarming and compelling way. I found it very enjoyable and I thought the not-quite-original characters (i.e. they were named in the Harry Potter books but didn't receive any characterisation) were all interesting and sympathetic, even those members of the Black family who were fairly dark and evil (because despite their many faults, their love for their family redeems them somewhat). It's funny and sweet and beautifully written.
I had only a few minor quibbles with this story:
1. I thought that Sirius Black kind of takes over the story when he's released from Azkaban, and some of the characters get shunted off to one side (I would have liked to have seen more of Marius and Clytemnestra, for example). But Sirius Black is a very cool character in his own right, so I'm not complaining too strongly.
2. It's not a completed fic: currently, 67 chapters have been written and posted on fanfiction.net. I think the latest story arc is weaker than some of the earlier ones. (But I should probably reserve judgement until the story is concluded- maybe it will hold up better when it can be read all in one go.)
3. I'm not sure I like this fic's portrayal of Dumbledore (I think he suffers from Flanderization), but I guess it doesn't really matter because Dumbledore isn't really a major character and he appears only rarely.
Apart from that, I really do like this fanfic. I would recommend it.