I love my NEX mirrorless cameras - and they can match DSLRs for image quality and definitely bring convenience and lightweight portability to the picture. But for me, even as a mirrorless lover, they don't replace DSLRs...they compliment them very well. Much depends on the shooter - the more specific your photography becomes in certain subjects, the less the mirrorless cameras can match the DSLR for overall design, speed, and control. As William mentioned, portraiture work, especially serious studio type stuff, will be more challenging with a mirrorless. For me, as a long-time wildlife and bird photographer, DSLRs are a clearly better tool for that type of work in many respects, including focus speed, focus tracking ability, buffer size, battery life, optical viewfinder for better panning and tracking a subject, and low light focus speed & reliability.
That's not to say things like portraiture and birding can't be done with a mirrorless camera - it can, and it does...I've even successfully used my NEX for birds-in-flight shooting which is one of the more challenging types. However, it took much more of my skill and instinct and a little extra effort and lower hit rate to do it, compared to my DSLR...the mirrorless just throws a lot more barriers in your path.
Someday maybe they'll be near-equals...but even their design alone will prevent them from ever replacing a DSLR for some folks - many of us who use DSLRs don't necessarily want it to be a lot smaller and lighter - there are inherent advantages to the large grips, large bodies with plenty of acreage for controls and buttons, heavier weight to help stabilize and counter-balance heavy lenses, and larger viewfinders and LCD screens.
I cannot forsee mirrorless compacts ever replacing DSLRs entirely for me, but I also know I'll likely never be without a mirrorless compact to compliment my DSLR. The future of 'mirrorless' might eventually be full bodied cameras with the mirror removed from the equation - maybe that beast may someday replace DSLRs as it can answer many of the deficiencies...but there likely need to be some technological advancements in electronic viewfinder technology before that will work for a majority of semi-pro and pro shooters.