The primary advantage of the SLR was that you can see the image as the lens is framing the image - a huge improvement over rangefinder systems (such as the Leica M). This allowed the use of super telephoto, wide angle, macro and tilt shift lenses to be much easer. The primary downside of the SLR was that it did not show you how the exposure was going to be recored on the film or digital sensor.
The mirrorless system eliminates that and now lets you see precisely how the image is framed as well as how it is exposed in real time *without* taking the image as the LCD and viewfinder are constantly reading from sensor. In addition you gain the possibility to handhold at much lower shutter speeds due to the mirror slap being removed and the on board sensor shift stabilization systems. DSLRs couldn't do this and relied on lens based solutions (Olympus & Pentax did have sensor shift stabilization, but it was niche and the market leaders Nikon & Canon relied on lens based stabilization). Another advantage is that with the removal of the mirror box, you can have short flange distances allowing new lens designs and lens interoperability. Nikon has the shortest flange distance in the industry and has support for just about every other lens mount out their (though through third party adapters - some with full AF capability also).
So the DSLR, except for maybe a few niche cases is old technology that is superseded in every single way. The interesting thing will be to see how the new mirrorless cameras effect the UI and ergonomics of the camera systems. So far, the pro level systems (Z9, R5, etc..) are all still for the most part using the DSLR form factor. Especially Nikon. I actually like this, but lets see what the future holds.