In circa 1983, the Gen Xers started making their own music known as Alternative (e.g., Sonic Youth, Camper Van Beethoven, Red Hot Chili Peppers). This alternative music was not New Wave, and was not popular enough to play on the commercial radio stations still controlled by the Baby Boomers.
As such, in the 80s, alternative music was (for the most part) played on non-profit college radio stations. Then in the 90s, this alternative music finally became mainstream as Generation X now controlled much of the commercial radio scene (e.g., starting with Nirvana, and Pearl Jam in 1990). As such, the term "Alternative music" lost much of its meaning and terms such as grunge and post-punk were soon coined instead.
That all being said, the main thing about this music is not a genre, but the generation of people that made it; Generation X.
And who is Generation X? Clearly, one of the oldest of them is Eddie Vedder (born 1964) of Pearl Jam.
One of the youngest of them is Brandon Flowers (born 1981) of The Killers.
Enjoy. P in California (Born 1964)