In the Schrodinger equation time is treated like a parameter. But there is no reason to think it has to be treated this way and there are attempts to put clock times on a more physical footing in quantum mechanics, especially in quantum gravity, e.g. http://arxiv.org/abs/gr-qc/9303020.

There are various problems associated with understanding relativity and quantum mechanics that involve time. But it's a bad idea to think of this as figuring out the nature of time. For an explanation of some of the problems see Physical Origins of Time Asymmetry edited by J. J. Halliwell, J. Pérez-Mercader, W. H. Zurek. The papers in the book discuss various problems, like time asymmetry in thermodynamics, time in general relativity, time in quantum gravity etc.