We show that correlation and entanglement dynamics of spin systems can be precisely controlled and engineered using only a small number of external physical control parameters. We first point out that the correlation dynamics of such systems can be understood in terms of spin-wave propagation, giving a simple physical explanation of the behavior seen in a number of recent works. We then extend this picture to more realistic translationally invariant systems prepared in product states. Since spin waves propagate according to a system's dispersion relation which typically depends on external physical parameters, this insight provides a convenient way to understand how dynamics can be controlled. We demonstrate these ideas in a simple example system, showing that correlations can be made to propagate in well-defined packets whose speed can be engineered in advance, controlled during the evolution, or even stopped altogether.