The terraforming of Mars is often cited when talking about far-fetched science fiction concepts. Terraforming is the name given to any general series of processes that turn an uninhabitable planet into a habitable one by changing the atmosphere and other aspects of the planet. Mars is the planet whose chemical composition is closest to that of Earth, so it is the planet of choice for terraformation.
Unfortunately, even the most optimistic estimates for terraformation of Mars are well over a human lifetime. However, those estimates are based on slow terraformation, the use of organisms to modify the planet. Organisms require a lot of care to keep them alive, and they are terribly slow and inefficient. If one were to use artificial means to terraform Mars, then it is quick terraformation, which only takes a few decades to finish.
Example timeline for quick terraformation of Mars: (start date: 2020)
2020: Four nuclear explosions, each timed two years apart, commence on Mars at the southern dry ice cap. The nuclear explosions release dark dust that spread over the ice cap, trapping heat, which eventually sublimes the cap, releasing 100 mb of carbon dioxide gas within eight years. Also a PFC factory will be set up, turning chemicals from the Martian regolith into perfluorocarbons. These powerful greenhouse gases will trap much of the Sun's heat, raising the temperature.
2028: Machines that utilize my "photosynthesis without plants concept will be utilized, turning the carbon dioxide from the atmosphere into oxygen and acetic acid. The electricity needed to operate the machine will come from nuclear fusion, or if we haven't figured fusion out yet, nuclear fission. At the same time, the nuclear fission/fusion power will go toward melting water ice in the northern ice cap.
2070: Goal for completion of terraformation. This is not a far-fetched goal. Because of the immense concentrated power available from nuclear sources, the terraformation will progress very quickly. By 2070, the atmosphere should be breathable, and there should be enough water for human and plant life on Mars.