Kurzbeschreibung: The main feature of physical (quasi)crystals is their point-like diffraction which indicates that their internal structure exhibits long-range order. In particular, for quasicrystals this constitute a surprising observation since their internal order is inherently aperiodic, i.e., is intermediate between periodicity and randomness. In this talk, I will show how dynamical methods can be used to study mathematical quasicrystals, in particular, with the help of (topological) dynamical invariants. Starting from symbolic configurations we will explain the basic concepts of a dynamical hull (shift space) and word complexity (topological entropy). Based on analogous considerations for quasicrystals this will lead to the notions of Delone/Tiling dynamical systems and patch-counting entropy. Moreover, using some basic physical observations, we will identify a class of dynamical systems which present itself as a very natural candidate for models of aperiodic order. For structural reasons, these systems have zero topological entropy. This motivates the need for introducing alternative dynamical invariants that work in this zero entropy regime and I will elaborate on this during the second half of the talk. This is based on joint work with G. Fuhrmann, T. Jäger, D. Kwietniak and D. Lenz.