Some interesting continua can be represented in several different ways as a shift invariant subset of the Hilbert cube. In fact, several different representations as Mahavier products can be found for some continua each displaying different dynamical properties. We will review recent results concerning dynamical properties such as transitivity, mixing, shadowing, and specification that are exhibited by the shift map on Mahavier product embeddings of the Cantor fan and the Lelek fan into the Hilbert cube.