What happened to Harry's grandparents?(from both his mother's and his father's side)Do we know anything about them?

Not much is known about them. I read somewhere that James's parents were older when they had him and they were rich and James was their only child. They also seemed VERY nice. They let Sirius stay at their house during the summer and even treated him like a segundo son. I am pretty sure that they died, because Harry saw them in the mirror of Erised. Lily's parents are a REAL mystery. They are never talked about, other then the fact that they adored Lily and were kind of mean to Patunia. My GUESS is that they are dead also. Because if they were alive, I would think that they would have got in contact with Harry.

Actually, if tu look on the Black Family árbol that J.K. Rowling created, you'll notice a couple on there named Dorea Black and Charlus Potter. It also states that they had one son, but it is unknown who it is. Many people, including myself, believe that the son was James Potter. So perhaps James and Sirius were distantly related.
Very little information is dado about this side of the family. Harry saw a grandfather among the various relations in the Mirror of Erised, but we haven't been dado any más than that. It would seem that all the Potter family were wizards, and that they're all dead (PS12). JKR has told us that there was nothing sinister about the deaths of Harry's Potter grandparents (TLC). Harry's grandfather Potter was in Gryffindor, like his son and grandson

No I don't think they were ever mentioned.

Both his mathernal and pathernal grandparents died. I think his mathernal parents died before his parents got married o when they did? Something like that.