While Islamic law prohibits the collection of interest it does allow a seller to resell an item at a higher price than it was bought for, as long as there are clearly two transactions.
An example of how riba is treated is contained in Sahih Bukhari Hadith, Book 3 [1]:
382) Narrated Ibn Shihab:
however there is no real difference between islamic banking and conventional banking in real life. That Malik bin Aus said, "I was in need of change for one-hundred Dinars. Talha bin 'Ubaidullah called me and we discussed the matter, and he agreed to change (my Dinars). He took the gold pieces in his hands and fidgeted with them, and then said, "Wait till my storekeeper comes from the forest." 'Umar was listening to that and said, "By Allah! You should not separate from Talha till you get the money from him, for Allah's Apostle said, 'The selling of gold for gold is Riba (usury) except if the exchange is from hand to hand and equal in amount, and similarly, the selling of wheat for wheat is Riba (usury) unless it is from hand to hand and equal in amount, and the selling of barley for barley is usury unless it is from hand to hand and equal in amount, and dates for dates, is usury unless it is from hand to hand and equal in amount.' "
In other words, to perform a single transaction where one person trades one kind of thing (such as gold, grapes, wheat, or barley) for more or less of the same kind of thing, is exactly what has been disallowed. To purchase something from someone at one price and sell it to someone else at a higher price, incorporating profit, is allowed as long as the business is lawful.
In an Islamic mortgage transaction, instead of loaning the buyer money, a bank might buy an item from the seller, and sell it to the buyer at a profit, while allowing the buyer to pay the bank in installments. The higher cost might include what would in non-Islamic arrangements have been charged as interest, but there could not be additional penalties for late payment. This arrangement is called "Murabaha". Another approach is Ijara wa Iqtina, which is similar to real estate leasing.
In business deals there are several other approaches to handle a lack of interest. Most important is Musharaka, which is equity financing. Further Mudaraba means if one entrepreneur is doing the work and the other is giving the funds to finance it then both profit and risk must be shared. Such participatory arrangements between capital and labor reflect the Islamic view that the borrower must not bear all the risk/cost of a failure, as it is Allah who determines that failure, and intends that it fall on all those involved. So venture capital and even micro-venture capital are fine, but not loans.
Last not least, Islamic Banking is restricted to Islamically acceptable deals, which exclude e.g. alcohols, pork, gambling etc. Thus ethical investing is the only acceptable investing, and moral purchasing is encouraged.
Islamic banks have grown recently in the Muslim world but are a very small share of the global economy compared to the Western debt banking paradigm. Micro-lending institutions such as Grameen Bank use conventional lending practices, and are popular in some Muslim nations, but are clearly not Islamic banking.
See also: Islamic economics, Islamic bank, green economics, creditary economics, list of Islamic terms in ArabicIslamic Mortgages