Claim is reported to carrier.
Claim is assigned to an adjuster.
Adjuster reviews claim contacts all parties (generally) takes recorded statements from all parties (including witnesses), requests police report if there is one.
Adjuster determines liability.
Adjuster determines damages (either writes estimate themselves, requests estimates, hires an independent appraiser etc).
Adjuster issues payment for damages, (including paying rental if so required)
If injury claim;
Adjuster (after completing all above), requests a medical authorization to gather medical reports/bills etc.
When injured party has been released from physician, and 'healed' adjuster offers and negotiates settlement.