I accidentally rear ended someone's car...what happens now?

I accidentally had rear ended someone's car. We looked at the damage, his car had none, and my entire license plate broke off. Of course, I will admit, it's entirely my fault. We exchanged insurance cards, contact information, took photographs, and photo ID's. We didn't call the cops because we were... show more I accidentally had rear ended someone's car. We looked at the damage, his car had none, and my entire license plate broke off. Of course, I will admit, it's entirely my fault. We exchanged insurance cards, contact information, took photographs, and photo ID's. We didn't call the cops because we were clueless on what to do and since there was barely any damage, we thought there was no point to get them involved. So, I apologized and we both departed. What happens from now?

What should I do? Do I contact my insurance provider? Are my premiums going to be raised? Does anything happened to my driving record? Do I wait for the other party's call? or their insurance to call me?
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