Your insurer will probably have guidelines on their website as to when, how and what to report. I’d check there first. They will also provide forms to guide you as to the nature of your report and the information required. (They’ll want a diagram, I expect, showing the location and arrangement of the vehicles involved, the location including nearby cross streets, etc.)
In general, however, the advice above is correct: Report to your insurer on their forms as soon as safe and convenient, also considering your mental and physical state. (It wouldn’t make sense to contact your insurance company – even if you were otherwise “safe” – if you were still very upset or bleeding in an emergency room, for example.)
In addition, as others have also mentioned, a police report may be required as well, depending on your jurisdiction and the rules that apply there. In most cases in the USA, the threshold dollar limit for “police report required” is not very high (and the estimates of damage that can be caused by even a slight collision are generally so high), so it’s nearly always a requirement, especially if there will be a claim. (If someone tapped your bumper and the damage was minimal, and there were clearly no injuries – and you trust the other driver to not inflate the incident into something that was your fault, and add fake injuries, etc. – then you might both walk away from it and take no action. I’ve done that.)
If any injuries can be claimed, then a police report is probably always going to be required. (And if you don’t trust the other driver to not inflate this claim and make it “all your fault”, then you should also file with the police. Otherwise you would also be charged – or could be charged – with “hit and run”, which is in all cases that I know of carries more severe penalty than “an accident”.)
If you live in a “no fault” state, then it will probably be your insurer who pays your claim, so the sooner you file with them, the better.