There's a well-known quote, something along the lines of: "If you think you understand quantum theory, you don't." Feynmann famously observed that no-one understands quantum mechanics.
After much hard work, hundreds of thousands of people have mastered quantum mechanics; fewer - but still thousands - have mastered its more advanced cousins, quantum field theory and string theory. The show-stopping problem I'm discussing here is not that the maths is hard, though it is. No, it's deeper than that.
Prior to quantum theory, we took it for granted that reality, the universe and all that, has a prior existence and that the job of physics was to describe its true nature. We do this by creating mathematical models which can be interpreted into 'objective entities out there', where the maths explains how those entities behave and interact.
Quantum Theory is not that kind of theory: its equations tell us only the probability of observing certain outcome via constraints such as Schrodinger's equation. But what is the reality behind hyper-accurate quantum theory? The maths doesn't tell us, but it surely can't be anything we're familiar with. Weird quantum phenomenon such as interference effects, superposition and non-locality make sure of that.
Some people think that's just the way it is: we'll be forever ignorant of the true reality of the universe and we should get over it. Many physicists, however, still seek a mathematical model which could reflect how the universe might be and which also makes quantum theory come out right. The Many-Worlds Interpretation and Pilot Waves are attempts which have not found much favour.
Recently, however, Nobel Prize winning physicist Gerard 't Hooft published some new papers advancing the case that the universe is fundamentally a 1+1 dimensional cellular automaton down at the Planck scale. He argues that our familiar world of phenomena emerges in a dramatically non-local way from this underlying reality. Surprisingly, this excited debate has been playing out over at the Physics Stack Exchange here amidst much understandable scepticism.