Glass transition is still an unsolved problem in condensed matter physics and chemistry. In this paper, we critically reexamine experimental data and theoretical interpretations of dynamic properties of various processes seen over a wide time range from picoseconds to laboratory time scales. In order of increasing time, the ubiquitous processes considered include (i) the dynamics of caged molecular units with motion confined within the anharmonic intermolecular potential and where no genuine relaxation has yet taken place; (ii) the onset of the Johari-Goldstein secondary relaxation involving rotation or translation of the entire molecular unit and causing the decay of the cages, to be followed by the cooperative and dynamically heterogeneous motions participated by increasing number of molecules or length scale; and (iii) the terminal primary alpha-relaxation with the maximum cooperative length-scale allowed by the intermolecular interaction and constraints of the glass former. Some general and important properties found in each of these processes are shown to be interrelated, indicating that the processes are connected, with one being the precursor of the other following it. Thus, a theory of glass transition is neither complete nor fundamental unless all of these processes and their inter-relations have been accounted. In addition to published data, new experimental data are reported here to provide a limited collection of critical experimental facts having an impact on current issues of glass transition research and serving as a guide for the construction of a complete and successful theory in the future.