What we know and what we don't know. There are 3 conventional schools of thought on Quantum Mechanics: there is the Orthodox position which is the Copenhagen interpretation of Quantum Physics who use the Schrodinger-Dirac formalisms based on Max Born's Statistical Interpretation of Quantum Mechanics (http://en.wikipedia.org/wiki/Copenhagen_interpretation) Heisenberg's Matrix formalisms were later shown to be mathematically identical to Shrodinger's Hilbert Space (abstract vector spaces with all the properties of function spaces) based mathematics. This school of thought maintains that quantum mechanics can only be understood in this way (from the observation of photons) and we'll never be able to figure out or understand the inner workings of what's really going on inside the atom. This school of thought is content with not knowing where photons come from during drops in energy states, and maintain that this is just the way it is. PERIOD.
There is the Agnostic Position, they don't care they just use what works and don't get involved in the debates or philosophies.
And then there is the Realist Position which is the one that Einstein and Planck took. Planck maintained that we needed to figure out how his constant was derived from deeper physics, but Heisenberg just rolled with it...
Einstein swore till his death bed that this interpretation of quantum physics was wrong, but could never figure out the answer to make everything work.
The argument rages on about the deeper physics of what is really going on, and what types of things will be unlocked once we finally do figure it out...
A paper on unsolved problems in Quantum Physics:
Top Ten unsolved problems in Physics: (one person's list anyway)
And of course this fun list:
Channel: Sci & Tech Channel