Maker-taker is an exchange or trading platform pricing system. Its basic structure gives a transaction rebate to market makers providing liquidity (the makers); and charges a transaction fee to customers who take liquidity out of the market (the takers).
Firms that "make" a trade happen by posting buy and sell offers are paid a fee, typically between about 20 cents and 30 cents for every 100 shares traded. Firms that "take" those shares are charged a fee. 
The maker-taker model is in contrast with the "customer priority" model. Under customer priority, any account identified as “customer” goes to the head of the queue for priority of fill, without paying a transaction fee to the exchange. The exchange stays in business by charging market makers fees for transactions and payment for order flow. The payment for order flow is paid to brokerage firms as an inducement to send their orders to a given exchange.
The maker-taker model in options trading came from a pricing model that was used by the equity market. Developed by Island ECN in 1997, it was designed by Joshua Levine to give liquidity providers an incentive to trade in markets where spreads are extremely tight. It rewards liquidity providers by giving them rebates, and it charges customers who remove liquidity from the exchange. Makers would get a $0.002/share rebate and takers would pay a $0.003/share fee. The exchange would get the difference which was $0.001/share. Maker-taker pricing is predicated on a penny-increment environment.
The maker-taker model was only adopted by the options exchanges fairly recently and has been controversial. After the Chicago Board Options Exchange (CBOE) got rid of customer transaction fees in May 2000, the idea of passing fees along to the customer has been anathema in the options market. There was a fear in the industry that charging customers for access to liquidity would inhibit the market's growth.
NYSE Euronext's Arca Options platform and Nasdaq OMX Group's NOM platform both use a "maker-taker" pricing system, as does the new options exchange launched by BATS. The Chicago Board Options Exchange and the International Securities Exchange both use the customer priority, payment-for-order-flow system. However, in March 2010 the ISE introduced a maker-taker structure for options on the PowerShares QQQ Exchange Traded Fund, Citigroup, Inc., and Bank of America Corporation.
Critics of the maker-taker model have argued that the fees might be giving brokers incentives to prioritize maker-taker fees over trade execution quality. Subsequent to a study by Woodbine Associates which highlighted the potential conflict of interest, Senator Charles Schumer requested that the Securities and Exchange Commission study the issue. In a speech April 2, 2014, SEC commissioner Luis Aguilar suggested the commission entertain "a pilot program in which maker-taker rebates would be temporarily prohibited for certain securities.”
ICE's CEO Jeffrey Sprecher has said the maker-taker model distorts pricing because there are rebates and other discounts that do not show up in the bid/offer, and that the trading noise created by the model has crowded out the price discovery process. Another criticism is that high frequency traders could take advantage of rebates by buying and selling shares for the same price in order to make money on arbitrage.  
In a June 17, 2014 hearing of the Senate Permanent Subcommittee on Investigations, NYSE president Thomas Farley said the exchange is "seeking support for the elimination of maker-taker." At the same hearing, Vanguard's Joseph Brennan also called for a "revisit" of maker-taker.
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