Exoplanets, short for `extra solar planets, are planets outside our solar system. They are objects with masses less than around 15 Jupiter-masses that orbit stars other than the Sun. They are small enough so they can not burn deuterium in their cores, yet large enough that they are not so called `dwarf planets like Pluto. To discover life elsewhere in the universe, particularly outside our own solar system, a good starting point would be to search for planets orbiting nearby Sun-like stars, since the only example of life we know of thrives on a planet we call Earth that orbits a G-type dwarf star. Furthermore, understanding the population of exoplanetary systems in the nearby solar neighbourhood allows us to understand the mechanisms that built our own solar system and gave rise to the conditions necessary for our tree of life to flourish. Signal processing is an integral part of exoplanet detection. From improving the signal-to-noise ratio of the observed data to applying advanced statistical signal processing methods, among others, to detect signals (potential planets) in the data, astronomers have tended, and continue to tend, towards signal processing in their quest of finding Earth-like planets. The following methods have been used to detect exoplanets.