The Most Mysterious thing in observable Universe

The problem arises when something we know and understand very well, suddenly becomes eerie. That is what's going on with KIC 8462852 aka Tabby's star.

To understand why tabby's star is an anomaly, we have to learn how kepler spacecraft works.
Keplar

Kepler Spacecraft has been orbiting earth since 2009 with one sole purpose: to discover Earth-size planets orbiting other stars. These Earth-size planets are light years away and emit no light. Hence Kepler has to observe them indirectly, by looking at the respective star the planet is orbiting.

Kepler's sole science instrument is a photometer that continually monitors the brightness of over 145,000 stars at a given time. So when ever a planet comes in between the star and the Kepler's photometer, the brightness of the star decreases. It looks something like this.

Notice how symmetrical the dip is

To put things in perspective a planet with the size similar to jupiter would decrease the brightness of the star by 1 percent

But KIC 8462852 exhibits strange behaviour. On 5th march 2011, star's brightness dipped by 15 percent!

The dip is asymmetric, hence it can't be a planet (sphere)

here is tabby's star on 28 February 2013

this looks strange

on 17 april 2013
WTF?

Here are some possible explanation

1. Younger star with coalescing material around it

But, spectroscopic study of the system using the NASA Infrared Telescope Facility (NASA IRTF) found no evidence for coalescing material within a few astronomical units of the mature central star

2. Planetary debris field

But, there is no observed excess infrared energy. Thus, ruling out massive planetary debris.

3. A cloud of disintegrating comets

This theory purposes that the gravity from a nearby star may have caused comets from KIC 8462852's Oort cloud to fall in-system

However, the notion that disturbed Oort cloud comets orbiting elliptically close to the star could exist in high enough numbers to obscure 22% of the star's observed luminosity has been doubted. Although this is the best non-alien explanation

4. Kepler is giving out false readings

The data from Kepler has been tested and cross examined by many people, and the consensus is that there is no error in the measurements

4 An artificial megastructures aka Dyson swarm

There may be a type II civilization out there who is sucking the energy of tabby's star. This would require an truely enormous structure to be build around the star like this

An explaination where aliens are involved, are generally frowned upon by the scientific community. As it is a last resort, if every other possible explaination fails then aliens are considered. And even if it is true there is no way to test this hypothesis unless aliens make contact with us.

Many astronomer are currently working on this problem, to learn more please read several paper written on KIC8462852