Basically it describes and explains interactions on the small scale (microscopic) of atoms and below (e.g. electrons, quarks).
It is not one of the fundamental theories that describe matter, but it is The fundamental theory that describes matter (note to physicists: this is an overly simplified generalization)
It is not a field by it self, it is just the most important foundation of modern physics, in other words, its the fundamental requirement to know before doing pretty much any research in physics.
It comes in two flavors:
1.) Non-Relativistic Quantum Physics: describe microscopic phenomena where the speed of objects or particles involved is way slower than speed of light.
2.) Relativistic Quantum Physics: Describes microscopic phenomena where things approach speed of light. It combines Einstein's Special relativity along with quantum physics. It provides some corrections to the basic theory as well.
An example of fields that are based on it: particle physics (relativistic quantum physics), solid state physics (non-relativistic quantum physics mostly used) and others.
There are no labs (to be specific,, the term research institutes or research groups is more widely used) dedicated to quantum physics, rather to the applications (be it theoretical or experimental), and there are so many of those world wide.
Fundamental research pertaining to the theory is rather limited right now.
As for people who use it, I can't specify that but it would suffice to say that scientists from different fields use it e.g. physicists, chemists.
As for breakthroughs, I am not aware of any "breakthrough", what you might read in the media is often written by journalists and not scientists where they often exaggerate over the importance of a recently published research paper.