Monitoring Starlight
Searching for alien life is a little more difficult than looking for a misplaced pair of socks due to the immense distance between here and absolutely anywhere. Many times, it appears simpler to focus on signs of alien life rather than aliens themselves. We've started observing starlight because of this.
Often, one of the only things we can observe from a far-off galaxy is light from distant stars. We won't be peering inside alien homes' windows, not even with the James Webb telescope. But merely by examining the light that reaches us, a star can provide us with a wealth of information about a certain solar system.
Not just their worlds, but even starlight, is examined for indications of alien technology. A large space station, for example, will throw a shadow, and we might be able to detect that shadow obstructing starlight as well. The concept is that a technologically evolved race would have developed great technological marvels, such as power plants the size of stars or computers the size of entire solar systems.
Because stars like the far-off Boyajian's star are prone to periodic dimming, scientists have begun to speculate if there may be extraterrestrial mega-structures interfering with the transmission of light from those systems to our own.
