I'm fairly new to bitcoin and I'm still trying to understand some of the basics, but I'm curious about what will happen when all bitcoins have been mined.
Over 120 years from now, when we're all dead? I'm sure they'll figure it out. I'm not concerned.
What will happen to all the "mining industry" that seems to drive the bitcoin world?
"Mining" is actually a popular nickname for "transaction processing". "Miners" confirm transactions into the blockchain, and in exchange for this service they receive a "Block reward" that is equal to the sum of the current block subsidy plus the transaction fees of all the transactions that they confirmed in the block.
The block subsidy is currently 25 newly created bitcoins every block. That subsidy is cut in half (and rounded down to the nearest satoshi) every 4 years. So, in 2016 the block subsidy will be reduced to 12.5 BTC, and in the year 2020 it will be reduced to 6.25 BTC, and so on.
Meanwhile, as bitcoin becomes more popular the total number of transactions will increase. This will result in more transaction fees for the "miners".
Eventually the amount of the block reward from transaction fees will be larger than the amount from the subsidy. Perhaps at that time we'll stop calling it "mining" and instead call it what it really is: "transaction processing". Instead of calling people "miners", we may start calling them "transaction processors".
In a bit over 120 years, the subsidy will drop from 0.00000001 BTC per block to 0 BTC per block. Long before that bitcoin will either have succeeded in maintaining security with transaction fees or it will be long since dead.