The Quran forbids riba, which is interest charged on loans, because it makes the lender profit without risk while the borrower in need may be crushed, and it spreads inequality. Muslims use instead profit sharing, trade, leasing and loans without interest.
The fuller answer
The Quran says God has permitted trade and forbidden riba, and it threatens those who do not give it up with war from God and His Messenger, which is a very strong warning. The Prophet ﷺ cursed the one who takes it, the one who pays it, the scribe and the two witnesses.
Islamic finance has grown into a global industry of Islamic banks, takaful (insurance) and sukuk (bonds), built on partnership and real assets. Muslims differ over some modern products such as mortgages, and many use Islamic home financing where it is offered.
Those who consume interest cannot stand [on the Day of Resurrection] except as one stands who is being beaten by Satan into insanity. That is because they say, "Trade is [just] like interest." But Allah has permitted trade and has forbidden interest. So whoever has received an admonition from his Lord and desists may have what is past, and his affair rests with Allah. But whoever returns to [dealing in interest or usury] - those are the companions of the Fire; they will abide eternally therein.
O you who have believed, fear Allah and give up what remains [due to you] of interest, if you should be believers. And if you do not, then be informed of a war [against you] from Allah and His Messenger. But if you repent, you may have your principal - [thus] you do no wrong, nor are you wronged.
O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent. And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.
