Once all the bitcoins are mined, miners will still be rewarded with some amount of bitcoins (although small), and this will be imposed as a small transaction fee upon those who are sending and receiving the cryptocurrency.
According to the bitcoin protocol, which Satoshi Nakamoto programmed, the reward miners get for successfully publishing a block will be halved every four years. This will go on for about until the 2100s. Only then will the mining rewards stop, or in other words, all the bitcoins will be mined out by that time.
But even then, miners, the people who keep the blockchain updated, and the entire system from crashing down, will be rewarded for their efforts and investments of time and computing power.