I don't believe there are too many making giant leaps forward in pushing the definitions of music. The borders have not been pushed, they have been removed. This does not limit anyones ability to create music, based on archaic systems or physical limitations, it allows people to create any kind of sound they want. The only progress we will see for sometime is new timbres being created.
We understand what produces the phenomenon of sound and therefore music. Obviously any pitches can be used, the only limits are the ranges of human hearing. We can put these pitches in any order, occurring at any point in time, this is basically limited to when you define the beginning or end of your piece, anything can happen in between. Timbres are limited only by imagination and experimentation, they lose uniqueness when our ear interprets it as white noise, a seemingly random sound or just highly complex tone.
I feel the most impressive strides in music will be made with texture that will be created, and plenty already have been. No doubt new sonic sculptures are being made currently on a myriad of mediums. There are countless ways to create new atmospheres of sound and express the endless ideas of man.
Music has been completely dissembled into its bare pieces, now the composer is able to pick which tools he wishes to craft his aural architecture. Defining one's own style based on the resources made available by past generations will allow more avenues of music to be discovered.
We have new breakthroughs in music, it happens with basically every band. They are an amalgam of different sounds, usually unique to their own group. Similarities are often seen and this is why artists will say they are a funk/blues/reggae band or a post-industrial-neo-doom or perhaps a grind/hard/goat/apple-core band... the permutations of existing genres and new coined terms is also endless... whether any of these are desirable is a matter of opinion.
As for a list of musicians that I feel are forging their own way into the ether of music:
Non-horse - acting as a DJ using cassette tapes he creates mind-blowing psychedelic effects, with circuit-bent hardware and field recordings of a nefarious nature, this is worth checking out.
The Skaters in a similar fashion to Non-horse/G lucas crane, these guys twist knobs and fluctuate air in a distorted chaotic fashion, yielding very interesting.
There are plenty of other artists, but in an attempt to not sound like a jerk listing off underground musicians I will stop there.
With what I know about music and the current state of the world, I feel things are bubbling below the surface, not yet noticed until the majority of people stop looking in the same direction for entertainment. While society is homogenized in one direction, a detritus is created due to the run-off. This is where the new inventiveness will come from.