Complex Metallic Alloys (CMAs) are metallic solids of high structural complexity, consisting of large numbers of atoms in their unit cells. Consequences of this structural complexity are manifold and give rise to a variety of exciting physical properties. The impact that such structural complexity may have on the lattice dynamics will be discussed. The surprising dynamical flexibility of Tsai-type clusters with the symmetry breaking central tetrahedron will be addressed for Zn6Sc, while in the Ba-Ge-Ni clathrate system the dynamics of encaged Ba guest atoms in the surrounding Ge-Ni host framework is analysed with respect to the experimentally evidenced strong reduction of lattice thermal conductivity. For both systems experimental results from neutron scattering are analyzed and interpreted on atomistic scale by means of ab initio and molecular dynamics simulations, resulting in a picture with the respective structural building blocks as the origin of the peculiarities in the dynamics.