Since their discovery around forty years ago, quasicrystals (QCs) have attracted substantial research interest due to their unique structure. Even so, there are still remaining questions in terms of why and how they form in the first place. Here, we present our efforts on tracking the nucleation and growth of QCs near- and far-from-equilibrium, by leveraging state-of-the-art dynamic imaging techniques. Our research was conducted with the aid of time-resolved synchrotron-based X-ray microscopy and dynamic transmission electron microscopy. By coupling these two techniques, we have investigated a broad range of length-scales (from tens of nm to hundreds of ým) and solidification pathways (1 K/s to 106 K/s cooling rates). The results provide a wealth of knowledge on the emergence of QCs in deeply undercooled melts; the influence of phasons on QC coalescence; and the growth mode of the QCs from a liquid (solidification) and from a solid phase (precipitation).