Is climate change (or global warming) happening?
NASA: Yes. The causes are complex (GHGs, volcanoes, solar, aerosols). NASA is monitoring many of these from space (SORCE, ACRIMSAT, MODIS, AQUA,TERRA, SAGE II and III, etc.), and working to understand their climate impacts. Temperature change since 1850 is about 0.6 deg C but is a function of many different "forcings" (incl. carbon dioxide).
NSIDC: In the past fifty years, the amounts of greenhouse gases (GHGs) such as carbon dioxide (CO2) and methane (CH4) in our atmosphere have increased rapidly. They now stand at levels far in excess of those indicated by deep ice cores spanning the past several hundred thousand years. A portion of today's CO2 gas contains a 'fingerprint' (i.e., its isotopic make-up) that is consistent with fossil fuel burning. Much of the data describing the ice cores is held here at the Ice Core Data Gateway, managed jointly by NSIDC and NOAA's National Geophysical Data Center.
Further, global warming (caused by a combination of many factors) is having an effect on the world’s ice masses. All but a very few of the mountain glacier regions on Earth are in decline. This decline contributes to the present rate of sea level rise, which is currently about 1.5 mm per year (about a sixteenth of an inch). Summertime sea ice cover over the Arctic Ocean is also declining, and in some areas this ice cover is thinning rapidly.