The earliest attempts used carbon based materials that absorbed radar signals instead of bouncing them back to the radar station. These efforts never made it past the testing stage, but in the 1950s, the U.S. U-2 recon aircraft used ferrite (iron impregnated) paint to reduce the aircraft's detectability. It was found that slightly changing the shape of some aircraft parts also reduced radar effectiveness. These techniques were carried over to the 1960s SR-71. But something else was discovered as well, that the Russians could improve their radar to overcome much of the stealthiness. It was a race, between the stealthy construction techniques and improvements in radar. In the 1970s and 80s the U.S. developed the F-117 (which depended more on the shape of the aircraft to bounce radar signals away from the transmitter that sent them) and the B-2 (which used shape and more radar absorbent materials.) Going into the 1990s, European nations are devoting more effort to electronic methods (sending out a signal that cancels the radar signal.)
If you use a stealth aircraft against an opponent who has not got the latest "counter-stealth" radars, your aircraft will be pretty stealthy. But you have to prepare for the worst, and Russia has established itself as the purveyor of counter-stealth radars. Russia has been working on stealth for 60 years. Never very successful in that department, they learned in the 1950s, when confronted with the stealthy U-2s, that adding more frequencies and computer assistance to their radars that they could overcome much of the stealth effect. Thus Russian surface-to-air missile systems are now selling not just because they are cheap, but because they are the best on the market for detecting stealthy aircraft. Or so the Russians say. Technical details of how stealth, and counter-stealth work are kept as secret possible. So far, the Russians have not had any opportunity to put their counter-stealth radars up against stealthy American aircraft. But it's only a matter of time.
"Stealthiness" (the ability of aircraft to hide from radar) is very popular these days. But it's an effort that's been going on for sixty years, and the radar is still winning. The reason the race continues is that stealthiness may not make you invisible to radar, but it will make you less visible, and this is a real advantage in combat. If an enemy radar takes too long to confirm that you are out there, you have enough time to get the first shot off (of an air-to-air or air-to-ground missile.) So being "invisible" to radar is not as important (and has proven impossible) as making enemy radar less effective.