There is a common perception that if human societies make the significant adjustments necessary to substantively cut emissions of greenhouse gases, global temperature increases could be stabilized and the most dangerous consequences of climate change could be avoided. Here we show results from climate model simulations with new mitigation scenarios for the future to illustrate that, with aggressive mitigation in two of the scenarios, globally averaged temperatures could be stabilized at levels either below 2C above pre-industrial or near 3C above preindustrial. Yet, even as temperatures stabilize, sea level would continue to rise due to climate change commitment. However, the future rate of increase of sea level rise would be ameliorated with aggressive mitigation compared to a scenario with little mitigation where future sea level rise would be large, and continue unabated for centuries. With aggressive mitigation in these scenarios, global temperatures can be stabilized, and though sea level rise cannot be stopped, it can be slowed down.