The Dyson sphere or Dyson shell is a theoretical megastructure that was first proposed by astronomer Freeman Dyson in 1959. This has been and will remain science fiction for a long time, but is interesting from the perspective of the total limit of energy a society can access. A Dyson sphere is a sphere approximately the size of a planetary orbit that would be able to harvest all the sun's energy and, on the inside surface, would be habitable to humans.
The sphere would be composed of a shell of solar panels around the star, making it so that all of its energy radiated would hit one of these panels, where its energy could be collected and used. Thus a Dyson sphere would create not only immense living space, but also gather extraordinary amounts of energy.
Building a Dyson sphere would be extraordinarily complex, if at all possible. Thus its conception assumed a super-advanced civilization. First, creating the shell would require superstrong materials with a tensile strength vastly exceeding any known material to ensure the sphere doesn't tear itself apart. In addition, the sphere would be gravitationally unstable. If any part of the sphere were moved even slightly closer to the Sun, its gravitational binding would be disturbed and part of the sphere would be pulled in towards the Sun.
Along with being complex to build, it would be difficult - if not impossible- to gather the materials that would be required to create the sphere. However, if one were to destroy and strip mine the entire inner solar system - Mercury, Venus, Earth, and Mars - enough material could be gathered to create the sphere with a radius of the Earth-Sun distance, 3 [m] thick.
Overall, the Dyson sphere is a bold theoretical solution to the energy situation that much more advanced descendants of Earth might face in the future. However, with current technologies it is entirely impossible to create.
This idea is probably best explored as science fiction, and quite naturally was. Larry Niven wrote the novel Ringworld as an exploration of how impossibly advanced it would be to build even enough of a Dyson sphere to act as a ring around the sun. This book won both the Hugo and Nebula (arguably the two most important science fiction writing awards) Awards for best novel published in 1970. For more information (and reviews) check out Goodreads.