In Newtonian physics, time is simply a parameter along which the variables of a system vary.
Einstein introduced a bit of frame-dependency with the development of special relativity, but he did not initially challenge time's fundamental role.
That would come from Minkowski, who, in 1908, proposed that relativistic physics is best understood as living in spacetime, rather than space and time separately.
Einstein was initially dismissive of this idea, calling it "superfluous learnedness", mere mathematical trickery.
He quickly came around to it though, and was heavily inspired by it in developing his grander theory of general relativity, fully published in 1915.
The value of the concept of "spacetime" is great, in my opinion, turning some previously contrived concepts into almost inevitabilities.
Lorentz transformations, originally a bizarre set of equations full of inverse square-roots, become simply rotations.
The whole theory of electromagnetism, which is convoluted in the Newtonian paradigm, becomes almost pure geometry.
General relativity is often considered the most beautiful theory in physics.
The 'conceptuaesthetic' appeal is noteworthy as well.
The idea of space and time being components of one object is fascinating in its own right, I think.
It is interesting as an overturning of one's instinctual sense of time, an alien concept which is nonetheless real, and makes all-too-much sense in hindsight.
It feels like deep progress, like a glimpse outside of anthropomorphic perception.
It's the good stuff.
Special relativity was not the only physics revolution of the 20th century, however.
There was also quantum mechanics (QM), which came with a much deeper paradigm shift.
The state of a system is no longer a particular configuration of particles or fields or whatever; rather, it is a distribution over all possible configurations.
This distribution, the wavefunction, is the thing that really exists, and evolves over time.
Early quantum theory was nonrelativistic, merely adapting the Newtonian ideas into the quantum framework.
Actually, Shrödinger had intially tried to make a relativistic quantum theory, coming up with what was later known as the Klein-Gordon equation,
which puts time and space on equal footing.
The equation did not make correct predictions, because as it turns out, relativistic QM is more difficult than that, so he didn't publish it.
Instead, we got the Shrödinger equation.
QM was eventually successfully made relativistic, through quantum field theory (QFT), which sits to this day as the ultimate framework we know of underlying all of physics.
The bizarre thing about it is that the concept of "spacetime" has been, in a certain sense (though not in another), abandoned.
Systems are modeled as wavefunctions, distributions over all configurations of a set of fields, which live in space, with the wavefunction evolving over time.
In this way, the quantum framework creates a fundamental rift between space and time.
Space is inside the wavefunction, time is outside it.
QFT is lorentz invariant, but it doesn't really put space and time on equal footing.
It is against, in some specific sense, the spirit of special relativity, though not strictly-speaking in conflict with it.
I am not a physicist.
But I wonder whether the future of fundamental physics will reconnect with spacetime.
After all, QFT's one major failure is general relativity.
Could quantum gravity involve putting time inside the wavefunction, to reunite it with space?
Apparently this more-or-less naturally comes about in the canonical quantization of general relativity, which gives the Wheeler-DeWitt equation.
I don't understand the details, but it's said that there are problems with it.
I imagine this conceptual leap might involve such a deep shift in one's intuitive understanding of time that many thinkers would reject the concept as incoherent.
I have no idea.
But I'm rooting for it, I guess.