Basically Polanski gave this 5th grade girl alcohol and raped her (this was about 30 years ago). He made a plea bargain for unsolicited sex with a minor, which is much lighter than what he would have gotten for raping a minor. However, when he found out that the judge might give him more years than what the plea bargain said he would get, he fled the country, rather than man up and face the charges for a crime that he committed.
Side note: he lost a civil suit to the girl and her family 30 years ago, and has yet to pay them any money. Loser.
Now what's going on with celebrities is that a bunch of them have been signing this petition to drop his warrant so he can come back to the states and get off without any sort of punishment. I even heard one person say that "he's done his time." Yea, he's done his time vacationing and partying and living in a mansion in Switzerland.
My internet was down last night, so I didn't get a chance to see if Natalie is a Polanski supporter.