The most famous institute in this field is S.E.T.I. and here is more about them from wikipedia:

The search for extraterrestrial intelligence (SETI) is the collective name for scientific activities undertaken to search for intelligent extraterrestrial life. For example, electromagnetic radiation is monitored for signs of transmissions from civilizations on other worlds.^[1][2]

There are great challenges in searching the universe for signs of intelligent life, including their identification and interpretation. As various SETI projects have progressed, some have criticized early claims by researchers as being too “euphoric”.^[3]

What do you think is the best way to search for aliens?  Feel free to comment with your ideas.