While there have been a number of good reviews on DFTB, in this review focuses on the application of DFTB to electronic-excited states, which has attracted significant attention for extending this computationally efficient approach to the time-domain. Although the field of chemical dynamics is incredibly vast, we concentrate our attention on the application of DFTB to real-time electron dynamics and non-adiabatic dynamics calculations. We first give a brief discussion of the underlying theory in each of these areas, followed by a didactic tutorial on simple molecules or model systems to show how these computational approaches and techniques are carried out in practice. These simple tutorials are written in a stepwise, instructive fashion to provide practicing researchers a detailed "look under the hood" to obtain a deeper understanding of how these techniques can be used to understand, probe, and even control the chemical dynamics of large systems. We then conclude each of these respective sections with a "real-life" application of these DFTB-based approaches on large dynamical systems to demonstrate their usefulness in contemporary areas of chemistry and materials science.