In the Newtonian model, time is an independent dimension. In the Einsteinian model, it is not independent of space, yet special. In the Feynman model, time is given by the individual trajectory of a sequence of particle interactions, and may be not aligned with the general arrow of entropy.
In my own understanding, there is no real space. The universe may simply compute on a graph structure, and space emerges at large scale information transitions in the graph. Time might be the result of computations, or rather, what the state changes of the local environment look like to a set of processes that have the necessary computational arrangements to observe that local environment. If time is the result of state changes, then time travel will be impossible.