Investigations of arctic ice-cores showed an increase of carbon dioxide concentration, the particulate matter and also of the mean temperature in the atmosphere. The objective of this thesis is to present several methods and processes to separate carbon dioxide from flue gases for sustainable sequestration. As a result the increase of carbon dioxide concentration in the atmosphere by emission can be reduced. The sequestration can either be terrestrial or marine. There are four options for terrestrial sequestration: 1) in depleted oil and gas reservoirs, 2) in saline formations and aquifers, 3) in minerals and 4) in unminable coal seams. For marine storage the carbon dioxide either dissolves in the seawater or forms lakes of hydrates in depths below 3000m. Health, safety and environmental issues have to be considered seriously. First of all, it is necessary to capture the carbon dioxide from the flue gas after combustion, in order to optimize the utilization of limited storage capacities. When capturing carbon dioxide the following processes will be discussed: 1) absorption using monoethanolamine, 2) pressure swing adsorption, 3) gas separation membranes and 4) the carbonation-calcination process. These separation processes lead to intense facility costs, which undergo an economic evaluation in this thesis.