Also the fact that dark matter and dark energy are unexplained by the Standard Model shows there are truly profound aspects of nature outside our current understanding: Standard Model - Wikipedia It is as if a geological researcher discovered most of the earth’s crust is made of an element that doesn’t fit on the periodic table.
The “decoherence” interpretation of QM has gained popularity in recent years. It treats superposition of states as a physically real situation, just one that is so extraordinarily fragile that it’s not observed at the macroscopic level. This has proven to be a useful model in such fields as quantum computation. In general, advances in nanotechnology have allowed experimenters to probe the boundary between quantum and classical behavior.
I don’t really understand what you mean by this and I suspect you do not, either. The “specific facts about particles” is the result of the interactons modeled and predicted quantum mechanics. Quantum field theories are a particular way of treating particles as an excitation in a fundamental field that are very useful, especially when trying to understand the interactions between multiple particles. All of physics is just waiting for someone to “conceive and publish”; it doesn’t exist as some kind of abstract framework unattached to the phenomena it models.
What you seem to be looking for is the “Eureka!” moment where some kind paradigm upsetting discovery comes along. Such discoveries are understandibly rare (and thankfully, because textbooks are expensive and poorly written enough as it is without having to cope with completely revising the underlying theories every few years). The apocryphal apple falling on Newton’s head situation almost never happens (and it certainly didn’t happen that way to Newton). In all of science there are perhaps a dozen such moments where previously unexplained or unconnected phenomena are unified in a novel comprehensive framework that was not previously considered by others working in the field, including Newton’s law, Maxwell’s equations, Einstein gravity (general relativity), lateral gene transfer, and perhaps endosymbiotic theory.
This is unsurprising since the only effects we see arising from dark matter and dark energy are gravitational effects with virtually no electrodynamic interactions, and the Standard Model says nothing about gravity. Whatever dark matter and dark energy emerge from is outside the scope of the Standard Model and current quantum field theories.
But we don’t need to go to atramentous observations to find profundity; ordinary gravity by itself is surpremely mysterious. We can certainly describe its effects, even in extreme conditions thanks to general relativity, but other than describing it as the distortion of an underlying plenum of space-time, we really don’t know what it is or why it works. And yet, we experience it with immediate directness every day.
Stranger
Quantum mechanics – at least the term – has been appropriated by the New Age/Paranormal crowd as a viable explanation for otherwise unexplainable phenomena. Although I’m reluctant to call this progress.
Advancements haven’t stopped by any means. Some are more technical nowadays, but not all. Just off the top of my head…
- fractional quantum hall effect, first observed and described in the 1980’s; totally unexpected before then
- BCS theory, worked out in the late 1950’s even though superconductivity was experimentally established long before
- topological order and topological phase transitions, a very young and dynamic field both on the theoretical and experimental fronts
- a large corpus of work recognized in the 2003 Nobel Prize related to superconductivity, superfluidity, and spontaneous symmetry breaking
- AdS/CFT correspondence and other dualities that have opened up new lines of theoretical work toward unified theories of nature
I stuck with “off the top of my head” because any attempt at an exhaustive list would lead to a very long post.
In general, lower dimensional systems (quantum dots and 1D and 2D gases), low energy systems, macroscopic systems, and statistical systems (i.e., those that can exhibit quantum phase transitions and emergent behavior) are the forefront of the field today. If we permit items that relate to the mathematical underpinnings of the Standard Model, then there were non-stop advancements in the theory through the last century. Indeed, particle physics was the canvas for QM advancement during that time. This continues today with grand unified theories and quantum gravity. And seemingly well-worn topics related to entanglement and coherence are still actively discussed and debated in the literature, in part because experiments continue to push us to regimes where previously unimportant considerations rear their heads.
Returning to the particle physics side…
Just writing down the postulates of QM doesn’t get you terribly far. Adding in special relativity and introducing variable particle number (quantum field theory) is a fundamental leap, but you then have a non-interacting theory unless you introduce more cleverness. Postulating that interactions come about not by arbitrary insertion of couplings into the theory but rather by requiring a certain type of symmetry in the Lagrangian[sup]1[/sup] is a big theoretical leap.[sup]2[/sup] Then you have a theory that might work but doesn’t allow for useful calculations, so you need to re-cast the whole thing in terms of perturbation theory. But then you don’t get meaningful results when you use your new theory, so you need to develop the idea of renormalization (which is indeed more than just math on top of existing math, so it’s meets your criterion). Quantum chromodynamics introduces a boatload of complexity at this point that you have to sort out, but this is probably across your fundamental vs. specific line. Along the way you have to deal with symmetries of nature being violated, each rather unexpectedly: parity first, then charge-parity. Also, your theory doesn’t permit masses where you need them, so you need to figure out a fundamental way to fix that through spontaneous symmetry breaking.[sup]3[/sup]
[sup]1[/sup] the expression that encapsulates all of the physics
[sup]2[/sup] Identifying the specific symmetry that describes our universe was also a big leap, but that would cross your line into talking about “our particles/our interactions”. But, the idea of having interactions come about elegantly in this way is a fundamental piece not implied by anything “upstream”.
[sup]3.[/sup] Hi Opal! 
There’s no difficulty in including relativity in quantum mechanics; the Dirac equation, for example, dates back to the 1930s. What distinguishes quantum field theory from quantum mechanics is seond quantization: promoting fields to field operators and introducing creation and annihilation operators, etc. One can also happily proceed with nonrelativistic quantum field theory (taking the spin-statistics theorem as axiomatic, presumably), though the objects studied with it are generally relativistic.
…and four days later it’s the subject of the physics Nobel Prize. The 2016 award just announced is in recognition of “theoretical discoveries of topological phase transitions and topological phases of matter”.
I was hoping for (and mostly expecting) it to go for gravitational waves.