A more thorough explanation:

Cap-and-trade is a system that limits the total amount of pollutants that a group of emitters can release by setting a "cap" on maximum emissions. It is a market-based policy that encourages businesses to invest in fossil fuel alternatives and energy efficiency to reduce overall emissions of pollutants.

Under a typical cap-and-trade program, the government sets a cap on the total amount of pollutants that emitters may release. The government then grants the right to emit pollutants through emissions allowances, which are licenses to emit pollutants. The total number of allowances is limited by the cap. Because allowances are tradeable, bankable, and scarce, they become a price signal for the cost of emitting when companies buy and sell allowances.

Emitters can use their allowances in several ways. They can design compliance programs to meet the emission reduction requirements, which typically include the implementation of pollution controls and measures to increase energy efficiency. They can also "bank" their allowance by choosing to hold the allowance for future use. Alternatively, they can sell their allowance to other emitters who pay value for the right to emit. When a price for emissions is set by a market, some emitters may choose to emit less than the amount authorized by their allowance. In that situation, emitters can "trade" their excess allowances by selling them in a secondary market.

The United States created its first cap-and-trade program in Title IV of the Clean Air Act Amendments of 1990 to regulate sulfur dioxide emissions through allowances. In 2005, the EPA released another cap-and-trade program through its Clean Air Interstate Rule (CAIR), which covers sulfur dioxide and nitrogen oxides. California was the first state to issue its program with the RECLAIM Program in the South Coast Air Quality Management District.

Internationally, cap-and-trade has played a role in reducing emissions. Under the Kyoto Protocol, a number of United Nations member countries established a cap-and-trade program to reduce greenhouse gas emissions. The Montreal Protocol successfully implemented a cap-and-trade program to reduce ozone-depleting substances. Europe achieved greenhouse gas reductions under its cap-and-trade program. Since the European Union's Emissions Trading System capped emissions from stationary structures in 2005, emissions reduced by 29% in 2018 since the program started.

However, the policy is controversial and has sprung numerous lawsuits in the United States. Many of the lawsuits have successfully repealed cap-and-trade laws. For instance, in North Carolina v. EPA (2008), the D.C. Circuit struck down the EPA's 2005 cap-and-trade program for being "arbitrary and capricious," "not otherwise in accordance with the law," and "fundamentally flawed." On the state level, California's cap-and-trade system for carbon emissions was challenged on the basis that it improperly created a tax due to the extensive amount of revenue raised from the auction of allowances. The state appellate court found the program valid since, inter alia, the auction system was not a tax because purchasing emissions allowances is a voluntary business decision, and the allowances are valuable and tradable commodities.