The amount of new bitcoins issued after every new block drops by 50% every 210,000 blocks. These events are called “halvings,” and Bitcoin is designed to have 32 halvings.
After the 32nd halving, bitcoin’s block subsidy will drop to 0.00000001 BTC for the next 210,000 blocks. Then it will fall to zero. At that point, the last bitcoins will have been mined.
Not quite 21 million
After the last fraction of bitcoin is mined, the total issued supply won’t be exactly 21 million. Yes, Bitcoin’s supply is capped at 21 million, but halvings and block rewards push this number slightly lower.
Halvings and block subsidy changes are completely predictable. Adding up the total amount of blocks and block rewards gives a sum of 20,999,999.98 BTC. This means that instead of a perfect 21 million, the actual number of total bitcoins that will ever be issued is slightly less than 21 million.
What happens next?
After the block subsidy falls to zero, network fees will be the sole source of income for bitcoin miners. Each miner will still claim a reward for solving each new block, but the reward will solely consist of fees instead of a mix of fees and a predetermined subsidy.