Understanding the Problem
One of the main challenges of global warming is that many aspects of the problem are not fully comprehended. Phenomenon such as positive feedback loops are poorly understood and often extremely unpredictable. Older ice, for example, reflects more sunlight than new ice, so when the old ice melts and then refreezes in the winter, the new ice does not reflect as much heat and melts more easily. There are potentially many other positive feedback loops, big and small, that researchers have not yet identified.
Political Support
Another of the largest challenges to enacting solutions to global warming is finding the political support to do so. The Copenhagen Accord of 2009, which was supposed to extend the earlier Kyoto Accord, was a failure by most metrics and did not end with any legally binding agreement. Some countries have committed to ambitious plans to lower their emissions, but others, like China, continue to ramp up the amount of carbon dioxide they emit, negating the positive efforts of others.
New Technologies
To have any chance of combating global warming, there must also be a concerted effort to develop new and better renewable energy sources. One of the main reasons that non-renewable energy sources are used so much is that they are cheaper and more convenient than the renewable alternatives. Geo-engineering technologies must also be developed, though not necessarily used. If human beings fail to enact any real solutions to global warming, there should be a plan B.
New Ways of Living
The most significant challenges of all with regards to global warming, however, are the changes that must be made to the lives of the average person. People everywhere must endeavor to drive less, buy groceries closer to home and use less energy in general. The root problem of global warming is that the human race uses too much, and if everyone does not cut back there will never be a long-term solution to global warming.