Welcome to the Bitcoin.com forums, Olodd!
As for your question, the answer (and much more!) can be found in the original Bitcoin white paper as written by Satoshi Nakamoto:
http://bitcoin.com/bitcoin.pdf
The short of it is: By the time all the coins have been mined in 2100 or so, blocks will be so large that the small fees paid by the billions of people using the blockchain will become the sole incentive for miners to keep finding blocks. The mining reward will no longer be needed.