The present day Martian climate is cold and dry, but a number of observations show surface features recording a history of running water. The amount of water that once existed was estimated as about 500 to 1000 m of the equivalent water layer. The presence of liquid water in substantial amounts at early times seems to imply a massive atmosphere with a heavy content of greenhouse gases. Where have the Martian water and greenhouse gases gone? The atmospheric escape to space is potentially important for the evolution of the Martian atmosphere. Understanding the way escape processes work in the Martian atmosphere at times in the past as well as at present is a fundamental issue when the evolution of the Martian atmosphere is studied.