Nemesis is a theorized red dwarf star--a binary companion to our sun. The case for Nemesis was first proposed in the eighties by Richard A. Muller, a Berkeley physicist, as a theory to help explain periodic extinctions on Earth. The theory grew from an observation by Luis Alvarez, Muller's mentor, extinction events on Earth were periodic, estimated to occur every 26 to 30 million years as evidenced by anomalous iridium deposits. Iridium is extremely rare but more common in meteors. This led to a hypothesis the deposits were due to meteors and their age corresponded with the so-called "extinction events". Alvarez invited Muller to debunk his conclusions.
Muller couldn't debunk Alvarez, and theorized, the existence of Nemesis, an as-yet-to-be-detected red dwarf star that varies in distance from 1 to 3 light years from the Sun. Nemesis crosses through an area of the Oort cloud, as the theory goes, where trillions of comets are present in a halo around our solar system. This infrequent pass by the so-called "death star" Nemesis, every 26-30 million years, displaces comets into the inner planetary orbits of our solar system. Lynn Yarris provided a good history of Nemesis theory's development in this Berkeley Lab publication.
Muller's theory has held up surprisingly well over the years. Sedna, a planetoid discovered in 2003 in the outer reaches of our solar system, whose orbit cannot be explained without the presence of another large body such as Nemesis.
In a more recent Space.com article, via Sign of the Times, "Nemesis Does the Sun Have a 'Companion'?" by Robert Roy Britt, Muller believes Nemesis "...is a common red dwarf star that would be visible through binoculars or a small telescope, if only we knew which of some 3,000 stars to look at. These are stars that have been cataloged, but their distances are not known". A visible star has only to be identified as the Sun's binary companion, as Muller sees it. Here is a link on You Tube to an eight minute excerpt of a History Channel show, where Muller discusses Nemesis. Muller wrote a successful book several years ago, "Nemesis the Death Star".
There are sky surveys that may provide answers in the near future? The good news is, according to Yarris, another extinction event is not due until 15 million AD!