EM waves are just the standard type of astronomy we've been doing for hundreds of years since telescopes were invented (millions of years if you just count eyeball astronomy). The best known form of EM is visible light, which is what we started out with of course. By the 20th century we started looking in other bands of EM, such as radio, infrared, UV, x-ray, etc.
Gravitational wave astronomy just got founded as of the year 2015, with our first ever GW discovery of merging black holes. We are now in the pioneering era of this type of astronomy much like Galileo was the pioneer of telescope astronomy over 400 years ago. GW astronomy is more like hearing something rather than seeing something. GW are set off by the loudest collisions and explosions in the universe. What vibrates if there's no air in space? Why it's the space itself that is vibrating. You can think of space as a type of material itself, and it conducts sound. But it takes some really massively powerful sources to get space to start vibrating.