We once thought that we were the centre of everything, as shown by Aristotle and Ptolemy, with their geocentric view of the universe. This then eventually developed into Alan Guth's view of an expanding universe, with the knowledge that neither we, nor even the Sun, are in the centre of the universe. Instead, we are getting further away from everything, seen by Hubble's observations of the redshift of the universe .
This notion that we aren't the centre of everything has led to a question of "Are we alone?". It has been widely explored in culture, from the martians in 'War of the Worlds', to E.T in 'E.T. the Extra-Terrestrial'. Our views of these illusive creatures have been both hostile and kind, yet we still have the urge to find out if they exist and where they live. Indeed, in a YouGov survey in 2015, when asked if they believe if there is extra-terrestrial intelligent life, 52% of the 1751 people surveyed said yes , showing just how embedded into our culture this hope for other life is.
Martians vs. Thunder Child by Henrique Alvim Corrêa
Little Green Men
With missions like the Mars Viking Lander, and projects like SETI (the Search for Extra-Terrestrial Intelligence), we have been scouring the universe to try and find life, or habitable conditions, on other planets and around other stars.
120 years ago, some believed that there was that intelligent life did exist on other worlds, and not only that but on our neighbour, Mars. Observations of the intricate canal system that laced the entirety of Mars to supposedly irrigate the crops on the drying world with water from the frozen ice caps . Some years later, it was deemed from observations from the 1976 Viking Lander Mission that this view was far from the truth, with life looking unlikely in today's world.
However saddening this was, we still had some hope, with searches continuing, like famous discoveries such as LGM-1 (Little Green Man). Jocelyn Bell and her team of scientist at Cambridge University discovered a strange radio signal which was a regular pattern of pulses of radio waves directed at them. They thought that it was possibly aliens, before realising the staggering reality that it was the first detection of a pulsar: a dense ball of spinning gas, with jets of gamma rays (high frequency light) streaming from its poles, being what was picked up by the radio telescope (they were radio waves because of the red shift of the waves from high frequency gamma to low frequency radio) .
First radio signal of Pulsar, examined by Jocelyn Bell. Credit: Billthom, CC BY-SA 4.0
'Like a Candy Store for Microbes'
WAIT Hunter (2008) 
The solar system, and indeed the universe, appeared to be empty of life apart from us, until we searched on not just planets, but moons: moons like Europa, orbiting Jupiter. This unlikely place was one identified by the Galileo spacecraft as having a salty liquid water ocean locked under the surface, which could harbour life. 
Water, being a key component in the search for life, has lead to many more places being identified as possible alien habitats, like Enceladus, orbiting Saturn. This moon was seen by the Cassini spacecraft, which flew through the plumes of vapour spewing from the alien surface. All key components for life were found, from hydrogen to carbon compounds . The only thing is, it's a very long way away!
False colour Cassini image of jets in the southern hemisphere of Enceladus. Credit: NASA
'Is There Intelligent Life on Earth?'
SAGAN C. (1994) Pale Blue Dot. New York: Random House