So, what do you think understanding is? In science, it generally means having models of the world that make correct predictions.
The photoelectric effect, Brownian motion, and the ultraviolet-catastrophe, were problems that stood out at the beginning of the last century which were explained. Plus many more things, like doped semiconductors, and superconduction. We have models for those that work, so we say we understand them. And the anomolous orbit of Mercury was explained by General Relativity.
We still have substantial outstanding problems, like dark matter and energy, the proton radius puzzle, the inside of blackhole event horizons and how Hawking radiation might preserve conservation of information, which Unruh radiation exists, whether entanglement means wormholes (ER = RPR), and many more. Eg
List of unsolved problems in physics. We can't know which might be the foundations of a new model, of new physics, until it happens.
Two things to understand about quantum physics. Uncertainty is an inevitable result of looking at systems where taking a measurement even with the smallest/lightest probe will disturb the system. And that fundamental particles can be literally indistinguishable, which has real-world consequences in Bose-Einstein and Fermi-Dirac statistics which govern bosons and fermions respectively. This is different to say a dice or coins, where we just choose to ignore differences. Like a blackhole, we only ha e certain limited 'handles' on them, and that can help us understand otherwise baffling behaviour like the Stern-Gerlach experiment.
What is missing? The Measurement Problem, or interpretations of quantum mechanics, is unresolved, but is usually argued to be for philosophy not physics because the proposals seem unfalsifiable. What governs the quantum coherence limit is the subject of intense interest for quantum computing which depends on increasing it. Possibly it's micro-scale gravity effects disturbing the system, and Bose-Einstein condensates in orbit or on the moon might identify that. And quantum-gravity, large masses at small scales.
Quantum Field Theory and the Standard Model are giant keaps forward in our understanding. That they have helped expose the scale of our ignorance, like about dark matter and dark energy, is part of that progress.