When I was studying Astrophysics at the University of Houston back in the mid-1980s, the favored theory to account for these periodic extinctions was a proposed brown dwarf or rogue star called Nemesis. Other competing theories proposed a Planet X (ten - before Pluto was slimed by the bumbleheads at the IAU. The Planet X theory is currently being subsumed into the proposed Planet IX (nine).
In any case, the theories propose a large body in the far reaches of the (non-existent) Oort Cloud that swings in towards the Sun every 26 million years or so, dragging a bunch of comets with it that pummel the inner Solar System - including Earth - and surround the Sun with a cloud of dust that temporarily dims the light. Thus, a one-two punch of heavy bombardment and reduced sunlight causes nearly every living thing on Earth to die off every once in a while.
Despite the fact that any number of probes, such as WISE, MASS-2, IBEX, and many others, have failed to find this killer star/planet, astronomers desperately cling to this idea, because for it to fail would drag down the entire framework of solar system formation, comet theory and even gravitation.
The Thunderbolts Project recently released a new video that explains this all quite well. The video does a good job of showing why the current sweetheart theories would collapse, but it glosses over some of the most interesting research - that of Thomas van Flandern.
Van Flandern was no lightweight in the heavenly realm. He was employed at the US Naval Observatory and is considered one of the greats in the field of orbital dynamics. The reason he is often top-shelved where no one can find his work is that he challenged almost everything held dear by the mainstream Einsteinian beanie caps.
Van Flandern calculated the orbits of thousands of short-term comets and asteroids and ran them back in time. What he found is that the vast majority of them converged at a single point between Mars and Jupiter at 3.2 million years ago and 65 million years ago. He theorized that the comets and asteroids were the result of one, maybe two, planets exploding (called Planet V/five and Planet K/Krypton).
Several things should be apparent at this point: 1) the location of these exploded planets is the current asteroid belt between Mars and Jupiter, and 2) the proposed explosions roughly correspond with the Pliocene and Cretaceous extinction events, respectively.
That these two points should just fall out of the data pushes the definition of coincidence, but it's not all the data available.
Van Flandern then took his data and began looking for other correlations across the Solar System. What he noticed was that a great number of planets and moons showed evidence of heavy bombardment and/or ash/dust/smoke. Earth's Moon has one hemisphere (Far Side - ahem) that is far more cratered than the other. Mars has one hemisphere that is more than 2km higher than the other, and the higher one is much more heavily cratered. The Saturnian moon Iapetus is coal black on one side and snow white on the other. The list goes on, but these are the most obvious and well-known observations. The one failing of Van Flandern's theory was that he could not propose a mechanism that would cause a planet to explode, though all the pieces fit quite well. This theory has come to be known as the Exploded Planet Hypothesis, or EPH.
Combined with the work of Immanuel Velikovsky, and researchers like Joseph Farrell and Richard C. Hoagland, the EPH has been fleshed out with anthropological and astrophysical evidence for such events. A thorough reading of these sources along with Van Flandern form a solid, multidisciplinary framework for the EPH.
The primary reason the EPH has been discounted and basically hidden is that the theory replaces the favored theory of planet formation, which sees comets as dirty snowballs/icy dirtballs left over from the formation of the Solar System. The idea is that when the Sun ignited, water was blown into the outer reaches of the Solar System, meaning that water should become increasingly prevalent as one moves away from the Sun. This collapses one of the major fairy tales in current "science," and starts a domino effect taking down many of the sacred cows in physics.
Even without all of the preceding, the search for Planet X has been a rather clouded one. It was first proposed to explain errors in the orbit of Neptune. When Pluto was discovered as part of the search for Planet X, it was quickly realized that the mass was not enough to cause the noted effects. It was later discovered that the errors were observational, and not real, and Planet X died out for a while. It was resurrected by Zecharia Sitchin in his somewhat questionable translations of Sumerian texts, and most recently was given a big shot in the arm by Mike Brown and his team, though now called Planet IX, which the Thunderbolts Project video linked above does a fine job of handling.
Astronomy and cosmology are rich grounds for personal education. The history of astronomy alone, what with Newton's occult practices and Tycho Brahe's silver nose, make for some great character studies.
More importantly, real science, based on observation and experimentation and not formulae and computer models, is far more interesting and challenging. It is also the part most closely guarded and hidden from public view, which makes any inquisitive mind perk up. It is usually the things that are denigrated, ridiculed and dismissed that hold the inconvenient truths.
How many more school kids would wake up and dive in if science was presented as something wide open to new ideas and discoveries, rather than rote required to be pounded in and regurgitated on command?
How many minds have we stifled with antiquated theories presented as stale facts?