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Ancient extraterrestrial civilizations, millions of years older than humanity, would need enormous amounts of energy. By creating a swarm of satellites in a spherical shell, they could harness much of the power of their star.
Science fiction author Olaf Stapledon described spherical, energy-trapping alien structures in his 1937 novel "Star Maker":
"Not only was every solar system now surrounded by a gauze of light traps, which focused the escaping solar energy for intelligent use, so that the whole galaxy was dimmed, but many stars that were not suited to be suns were disintegrated, and rifled of their prodigious stores of sub-atomic energy."
Talk by Stuart Armstrong, at the Oxford physics department
Abstract: The Fermi paradox is the contrast between the high estimate of the likelihood of extraterritorial civilizations, and the lack of visible evidence of them. But what sort of evidence should we expect to see? This is what exploratory engineering can tell us, giving us estimates of what kind of cosmic structures are plausibly constructable by advanced civilizations, and what traces they would leave. Based on our current knowledge, it seems that it would be easy for such a civilization to rapidly occupy vast swathes of the universe in a visible fashion. There are game-theoretic reasons to suppose that they would do so. This leads to a worsening of the Fermi paradox, reducing the likelihood of "advanced but unseen" civilizations, even in other galaxies.
Are there ANY present programs/probes actively searching for either these spheres?
A Dyson sphere is a hypothetical construct of a star purposely shrouded by a cloak of broken-up planetary material to better utilize all of the stellar energy. A clean Dyson sphere identification would give a significant signature for intelligence at work. A search for Dyson spheres has been carried out using the 250,000 source database of the IRAS infrared satellite which covered 96% of the sky. The search has used the Calgary database for the IRAS Low Resolution Spectrometer (LRS) to look for fits to blackbody spectra. Searches have been conducted for both pure (fully cloaked) and partial Dyson spheres in the blackbody temperature region 100 K
When one planet is no longer enough for a civilization, perhaps instead of growing their territory they shrink themselves into a computer simulation. If you could compute consciousness and reality perfectly, there is no real requirement that you go through the motions. We might find out that 99% of the life of the average civilization plays out in a shoebox drifting through empty space long after their star and their biology are gone.
The main issue i see with dyson spheres would be where the hell would ANY civilisation acquire the sheer quantity of raw material needed to construct one never mind keeping it stable relative to the variable forces emanating from the star enclosed.