Thousands of man-years of work has gone into climate modeling in the past few decades. With all that work we are getting better and better at modeling climate change, and indeed IPCC estimates (which use large interdisciplinary models) are becoming more and more accurate, and are matching observed temperature rises quite accurately. One of the reasons for this is that the basic inputs to the models (insolation, reduction of re-radiation, changes in albedo, changes in gas concentration) are easy to measure. A second reason is that we now have decades of models to compare with predictions, and so we now know what works and what doesn't. There are, however, two uncertainties that limit how accurate any model can be as the prediction time is extended. One is human behavior. Like the stock market, the future climate is dependent on human behavior. For example, a future where we return to emitting a lot of high altitude aerosols while dramatically cut down on CO2 production will look very different than a future where we avoid high altitude aerosols and decide to abandon renewable energy and efficiency standards in faavor of cheap coal. The second factors are nonlinear feedbacks. These are feedbacks that change with the temperature. Thus even though we may have an understanding of what they are doing now, we don't have a full understanding of what they will do when the temperatures increase. Some of these are pretty straightforward, especially on the negative side, For example, re-radiation will increase as temperatures climb. Since blackbody radiation goes up as the fourth power of temperature, there is a strong negative feedback that will, for example, prevent temperatures rising infinitely high. As temperatures climb, the Earth will radiate more heat until we reach a new equilibrium at a higher temperature, Others include chemical weathering (rocks, concrete and other minerals react with CO2 and take it out of the atmosphere) and biological uptake (higher CO2 levels = more plants = less CO2.) The positive feedbacks are a lot more worrisome. One common one is methane release from frozen sequestration (tundra, clathrates.) As these materials melt methane and CO2 are released, and methane is a strong greenhouse gas. (CO2 is relatively weak in comparison.) Thus more methane = more temperature increase = more melting = more methane. Another is albedo change; as snow and ice melt, darker surfaces are exposed to the Sun and absorb more heat. A third category of feedbacks are as yet unknown, since they can drive the climate in either direction. Daytime clouds greatly decrease albedo and lead to cooling. Nighttime clouds trap heat and lead to warming. Thus, an increase in cloudiness (likely as the Earth heats up and more water evaporates) can drive climate in either direction, depending on the time of cloud formation - and we don't have a good predictor of that, That uncertainty, on the surface, is a bad thing because it leads one to believe that we can't predict what will happen in the future. Fortunately, we have some other tools - behavioral observation. In engineering, we often design structures that must be kept stable with feedback loops (flight controls, electronic amplifiers, hydraulic systems.) The rigorous way to analyze whether a system will be stable is to do a control system analysis - figure out the expression that describes the system, plot the poles and zeros and look for basic indications (poles on the wrong side of the plot) that indicate the system is unstable. In many cases, though, engineers cannot do that, since they do not always know everything about the system. In a hydraulic system, for example, you may not be able to account for the exact amount of air in the system - and that affects compressibility of the fluid and hence overall system response. Fortunately they have another option - testing the system. Through either accurate simulation or actual testing, they can build the system and see if it's stable. The most useful method of testing is to apply a stimulus - a step or an impulse - and see how it responds. If it stabilizes at a new level it is stable. If it starts increasing and does so without limit, it is completely unstable. If it "rings" (oscillates) it is dynamically unstable. Thus by testing the response of the system, you can learn a a lot about it. We cannot (or more accurately should not) do that to the Earth. However, we are fortunate in that we have historical proxy records in the form of ice cores, sedimentation, tree growth rings etc that allow us to see what has happened in the past. Thus we can look back in time at other "step changes" in the climate and see how the planet has reacted. One of the big worries for some is that the climate is inherently unstable. Give it a step change and first all the methane is released from melting permafrost, and that warms us 20 degrees. Then the oceans evaporate, and all that water in the atmosphere traps all our heat and raises it another 50 degrees. Then some of the water turns to steam and that raises the temperature even more. (Same fear for the other direction - it snows, the snow reflects more light, it gets colder, it snows more, the oceans freeze, it gets colder still etc.) In an inherently unstable climate, a large enough step change will cause an irreversible slide in one of these directions as the positive feedbacks outweigh the negative ones. Fortunately, in our entire 4.5 billion year history, that has never happened - and that is a strong argument for negative feedback dominating over positive feedback in the long run. However, there are good indications that positive feedback is a significant event in the short term. We have seen several rapid warming periods where a step increase (caused by, for example, an increase in insolation) activates some of the above-mentioned positive feedbacks, and for a time the Earth sees a rapid increase in temperature. The biggest one of these, the Paleocene Eocene Thermal Maximum, resulted in a 6 degree C rise in temperature - higher than almost every conceivable scenario that we could drive by 2100. Fortunately, that data shows that those positive feedbacks are eventually swamped by the negative feedbacks. One of the strongest drivers of this is likely blackbody radiation. It is a small negative feedback at first, but since it increases by the fourth power of temperature, it very rapidly becomes significant and slows down further temperature rise - and thus the Earth stabilizes at a new, higher temperature. So overall the news is pretty good. If anything, we have learned that although we certainly have the power to change the climate by driving modest climate changes (2-3C worldwide), we don't have the power (yet) to send it to either deadly extreme. Whether or not we want to make those 2-3C changes, of course, is still an excellent question.