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In 1898 it is claimed that Nikola Tesla built a radio transceiver designed for communication with extraterrestrial intelligence. It has never actually been proven if this is a claim based on reality, delusion or braggarts bravado. In 1899 he claimed to have detected coherent radio signals which he believed came from Mars. 
Tesla died at the age of 86 in 1943 and much of his science died with him.
Project Ozma and Ozma II  of the 1960s searched for radio broadcasts from alien intelligense. Two nearby Sun-like stars, epsilon Eridani and Tau Ceti were targeted and no intelligent signals were discovered.
In the 1970s The Wow! signal was received. The Wow was a strong narrow band radio signal detected by Ohio State University's Big Ear radio telescope in 1977. It has been used as a talking point in the search for extraterrestrial intelligence. The radio signal bore all the hallmarks of intelligent extraterrestrial origins.
Multiple conflicting theories have been put forth on the signals origins including natural and intelligently made sources, but none have adequately explained it. The Wow! signal has been the strongest candidate for an alien radio transmission ever detected.
40 years after the WOW signal SETI detected 15 fast radio bursters. they are rapid pulses of radio energy that have been traced to an object known as 'FRB 121102'. 
Fast radio bursters have been deteted before but as singular one time events from scatterred locations. FRB 121102 has erupted at least 15 times. The repetitious bursts are viewed by some as a sign of intelligent design.
FRB 121102 is in a small galaxy long ago and far away. Far away as in 3 billion light-years away and long ago in that the radio bursts initiated when single celled life forms were just beggnning to evolve here on Earth.
The most titillating notion regarding these Fast Radio Bursts invokes the theory that they are from an advanced intelligence . While that is certainly feasible it is not the only possible explanation.
'It's very funky how the individual bursts can pop up anywhere in this wide range of frequencies, even though each individual burst has a relatively narrow frequency coverage ..... I have yet to see anyone offer up a good explanation for how that might happen.' Peter Williams of Harvard University
Harvard researchers have also speculated that these Fast radio bursters could be beams set up to potentially power light sails of extraterrestrial craft.
Another source of unexplained radio waves from space come from a small red star dubbed Ross 128 , about 11 light-years from Earth. The signals were detected by researchers at Arecibo Observatory in Puerto Rico led by Abel Mendez. Researchers are fairly certain that the radio waves originate in deep space.
Mendez does not believe the signal originated from extraterrestrial intelligence, but still can't explain it's origins despite multiple theories. The likelihood is that it is from a geostationary satellite.
1. A SIGNAL FROM MARS TESLA'S COLLECTED ARTICLES ON ALIEN COMMUNICATION
2. "Project Ozma was a search for extraterrestrial intelligence (SETI) experiment started in 1960 by Cornell University astronomer Frank Drake, at the National Radio Astronomy Observatory, Green Bank at Green Bank, West Virginia. The object of the experiment was to search for signs of life in distant planetary systems through interstellar radio waves. The program was named after Princess Ozma, ruler of the fictional land of Oz" - Wikipedia
3. Focus on the Repeating Fast Radio Burst FRB 121102
4. Ross 128: Scientists Solve Mystery of Radio Signals Coming from Nearby Star