Carbon cap and trade systems are plans in which countries, provinces, states and even cities set regulations (a cap) on the amount of carbon dioxide and other greenhouse gas (GHG) emissions industries/ power plants can emit, and then implement an Emissions Trading System (ETS). Companies included in cap and trade systems, often companies that operate power plants, have a limit (cap) on the amount of GHG emissions they can produce that is set by the government. Governments may either "grandfather in" GHG allowances (essentially give away credits based on past GHG production) or auction allowances off. Companies with extra carbon credits because their plants go under the limits can then trade their excess carbon allowances to companies that need to buy carbon credits to avoid going over the limit.

Auctions for carbon permits (one carbon permit is usually = to 1 metric ton of GHG pollution) are an essential part of the carbon cap and trade system, helping to establish a price on carbon, and are  much more effective than the system where credits are just '"grandfathered in". The cost of carbon permits is essentially the price of carbon. As GHG emission credits are auctioned off, a price on carbon is established. Companies can also keep carbon credits for future use in trading or for their own allowances. For companies that run over their GHG emissions limits and don’t cover their allowances, a heavy fine is imposed. Carbon cap and trade systems are designed to lower the cap annually, gradually reducing the allowable limit of GHG pollution for those industries targeted by the cap and trade system.

There are trades that offset GHG emissions; trades for credits with companies that have forestry projects and that are reforesting areas or that limit deforestation, or companies that have livestock projects that incorporate sustainable practices, or companies that invest in clean coal technologies such as carbon capture and storage (CCS) or other carbon sequestration measures. To make cap and trade systems even more effective, there should be more offset credits allowed for trades with companies that implement GHG emission saving and energy efficiency technologies like renewable energy, integrative gasification combined cycle (IGCC), and anaerobic digestion (AD), combined heat and power (cogeneration) (CHP) etc…

For some companies, it might make more financial sense and be more cost-effective to make the effort to reduce emissions through emission saving and energy efficiency technologies and/ or expanded use of renewable energy, and then sell their allowances to companies that are over their GHG limit. However, usually most companies tend to buy carbon allowances if it’s cheaper to buy them than to try to lower emissions. Carbon permits can be invested in by businesses, industries, or even the public in some regions, via a carbon futures market. 

Carbon cap and trade systems are in effect in about 40 countries and 25 states/ provinces/ cities globally. The largest market for cap and trade is in the EU with the European Union Emissions Trading System. The EU ETS covers more than 11,000 power plants and industrial stations in over 30 countries, as well as airlines (for flights within Europe until 2016). The primary focus of the EU ETS is to fight climate change by lowering GHG emissions.

The EU ETS remains the largest (and first) international trading organization for trading GHG emission allowances. The EU ETS has successfully put a price on carbon, with its system of trading allowances of GHG emissions, and has also watched GHG emissions fall by a few percent annually since it began in 2005. The cap, or limit, set on GHG emissions will be, on average, over 20% lower on all power plants and industries by 2020 from 2005 levels (when the program started), as the EU continues to make efforts to reduce pollution.  Clean, energy efficient, low-carbon technologies like CCS, IGCC, CHP and AD, as well as renewable energy, have grown in popularity throughout Europe, in part, because of the rising price of carbon resulting from cap and trade programs.

All countries deal with cap and trade differently. Most have cap and trade for industry and power sectors. South Korea has cap and trade for heavy industry, power, waste, transportation and building sectors. China has six provinces testing out cap and trade, and along with South Korea, represents a very large carbon market (with just those 6 provinces China is a large market, the entire country represents the single largest carbon market, by far). The U.K., Ireland, Iceland and the Scandinavian countries Norway, Sweden and Finland have legislated both a carbon tax and cap and trade programs.

The nine state agreement in the U.S. northeast (the Regional Greenhouse Gas Initiative, RGGI) is another major carbon cap and trade trading pact, and is, at least partially, based on the pioneering EU program. These states have auctioned off carbon allowances to industries in RGGI states, and have thereby collected well over $1 billion from carbon cap and trade programs, much of which has been reinvested in energy efficiency, renewable energy and other clean energy programs. Since carbon cap and trade has started in the U.S. northeast, GHG emissions have steadily dropped. Like the EU, this in part due to investment in clean energy technologies, but also because some companies in the U.S. northeast have switched from dirtier fossil fuels like coal to cleaner natural gas generators in power plants, or to renewable energy.

Some carbon cap and trade markets are:

EU ETS:

http://ec.europa.eu/clima/policies/ets/index_en.htm

https://www.youtube.com/watch?v=yfNgsKrPKsg

The U.S. Northeast region:

https://www.bostonglobe.com/business/2015/07/14/carbon-caps-help-northeast-economy-report-says/jPcTMPG6f6SjcRU8CBCSnO/story.html#

http://insideclimatenews.org/news/14072015/cap-trade-shows-economic-muscle-northeast-13-billion-RGGI-clean-power-plan 

"To comply with the federal Clean Power Plan's requirements for cutting carbon pollution from power plants, states have several options—including joining RGGI or similar schemes such as California's cap-and-trade system." – from: Cap & Trade Shows Its Economic Muscle in the Northeast, $1.3B in 3 Years (Regional Greenhouse Gas Initiative offers blueprint to all states as they begin to think about how they will comply with Clean Power Plan.) By Naveena Sadasivam, InsideClimate News

The RGGI states and California are ahead of the curve as far as complying with the Clean Power Plan.

California, Quebec: 

http://daily.sightline.org/2014/05/22/17-things-to-know-about-californias-carbon-cap

http://www.huffingtonpost.com/rosaly-byrd/an-introdu put a quotaction-to-carbon-cap-and-trade_b_6737660.html

Please also see: Carbon Tax - a levy on pollution whose time has come