Abstract This paper contains new views about the amorphous and partially ordered phases of the three polymers listed in the title. The discussion is based on information on structure, thermodynamic stability, and large-amplitude molecular motion. Polyethylene is the basic backbone of all alkene polymers, and the other two are the first members of the vinyl polymers which have stereospecifically placed alkyl side chains. Their multiphase structures consist of metastable crystals, mesophases, and surrounding rigid and mobile amorphous fractions. All these phases have sizes ranging from micrometer dimensions down to nanometers. Besides the phase structures, information about the molecular coupling between the phases must be considered. Depending on temperature, the polymer phases can vary from solid (rigid) to liquid (mobile). New knowledge is also gained by cross-comparison of the title polymers. The experimental information was gained from (a) various forms of slow, fast, and temperature-modulated thermal analysis to identify equilibrium and non-equilibrium states, (b) measurement of structure and morphology at various length scales, and (c) tracing of the large-amplitude molecular motion, the kinetics of order/disorder changes, and the liquid/solid transitions (glass transitions). It is shown that much more needs to be known about the various phases and their coupling to characterize a given polymer and to fine-tune its properties for a given application.