How to identify vaults and markets eligible to rewards?
The vaults and market eligible to rewards are identified with a three little blue stars logo: 
You can hover on the APY (for a vault) or the Borrow rate (for a market) to see the breakdown of the rate featuring potential rewards:
How to monitor and claim my rewards?
You can monitor your rewards (claimable and accruing) in the top of main Earn and borrow pages on your position recap section.
You will access the rewards details and claim by clicking on the "Rewards" button:
How rewards are distributed on Morpho?
Rewards on Morpho are distributed via Merkl.
Alternatively, one can monitor and claim its rewards via the Merkl app.