The decisions they make will have a major impact on how we live our lives and those of future generations.
Scientists have warned that if greenhouse gas emissions continue to rise, we will pass the threshold after which climate change will become catastrophic and irreversible.
That threshold is two degrees Celcius above pre-industrial levels, and scientists say a rise in global temperatures must not exceed that figure by the year 2100.
But delegates face a number of problems. Although many countries have already made pledges to reduce their greenhouse gas emissions in the run-up to COP 21, it is likely they will not be enough to slow global warming to two degrees.
The second problem relates to the differences between developed and developing countries. Developing nations want financial aid to help them implement the policies that will be a part of any Paris deal.
So, with so much at stake, can leaders reach an agreement in Paris?
Displayed with permission from Al Jazeera