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 global coupled climate model simulations with the new representative concentration pathway mitigation scenarios to 2300 to illustrate that, with aggressive mitigation in two of the scenarios, globally averaged temperature increase indeed could be stabilized either below 2 degrees C or near 3 degrees C above pre-industrial values. However, even as temperatures stabilize, sea level would continue to rise. With little mitigation, future sea-level rise would be large and continue unabated for centuries. Though sea-level rise cannot be stopped for at least the next several hundred years, with aggressive mitigation it can be slowed down, and this would buy time for adaptation measures to be adopted.