Summary: An electron-positron linear collider is presently the favorite option for a future particle physics facility at the energy frontier. Different concepts for such a facility are being studied in Europe, the United States and Japan. The Compact Linear Collider (CLIC) is being developed at CERN as a possible future project beyond the LHC. The CLIC concept is based on an innovative two-beam acceleration scheme, promising the generation and collision of nanometer-size particle beams. The high accelerating gradients of CLIC would reduce the size of such a facility and allow for an energy reach of up to 3 TeV center-of-mass. The basic scheme of CLIC, its promises, its challenges and its past achievements are explained.