Einstein said time is an illusion; funny, because he also merged time and space together to create timespace for his early theories. Was he confused? Not really, just contemplating concepts that had gotten more clear over time.
Time is not an illusion "because the past and future are happening right now," as someone recently tried to convince me, but instead, "because the past and the future do not exist." In other words, there is only the moment now, continually changing.
There is no reference to time in fundamental physics formulas. Time is not a feature of physics. Brain studies prove "the past" and "the future" are ways of organizing information which our brains do, but other than that, time does not exist. Only the now exists. What this means to the concept of timespace is a little mind-stretching to consider, so to keep things simple, let's stick with the fact that past and future are features of the mind, not of physics.
This is why the eventual advent of time travel will be a development within psychology, not involving physics as it is typically portrayed with "time machines" like the Tardis. No, time is not wibbly-wobbly, as Dr. Who describes it, at least not in a way that a machine can navigate a person using laws of physics.
However, although time machines like the Tardis will never be built, something very similar to time travel will soon be technically possible due to immersive virtual realities that can emulate other time periods. These are crude now, but will improve over time, and within a century a person will be able to travel to any time in the past and interact with famous avatars, like Mark Twain or Julius Caesar, rendered in technicolor 3D by AI, which will be able to manifest very sophisticated versions of these famous people, and everything around them. In fact, there will be competition between different flavors of AI, for which one has the most realistic time travel experience, kind of like the way movie studios compete for the best movies today. Eventually there will be court disputes over these things and thus a canonical "version" of ancient history will be developed and maintained by well-regulated AI, in order to provide answers to time-related questions that arise in courtrooms.
By then, we will hopefully have resolved issues like what is happening these days with Wikipedia, where special interest lobbies are able to change facts to fit their agenda, by simply employing lots of crowdsource editors who ensure their agenda makes it into the canonical version.
We will have resolved such things because the gap between virtual reality and real reality will have gotten so small that they blend together seamlessly in the places where they join. These will be regulated by openly-inspectable algorithms that change very slowly over time, to ensure stability, again, likely arising from courtrooms and other slow-moving legally-liable situations where such auditable stability is required.
There will, of course, be time travel in the virtual reality worlds back to the time of dinosaurs, and to other places in the universe, etc., and other absurdly impossible adventures, basically whatever you can imagine, like the holodecks out of Star Trek.