For the first time, an attempt has been made to illustrate the diversity of different forms of mesomorphism in flexible-and rigid-chain linear polymers whose macromolecules do not contain mesogenic groups. The emphasis has been on description of new structural varieties that are equilibrium mesophases from the thermodynamic viewpoint. Concrete examples of unusual two-dimensional and one-dimensional forms of ordering, recently found by the authors for a number of high-molecular-weight compounds, have been given.The originality of modern concepts of the structure of high-molecular-weight compounds (HMWCs) lies in the increasingly greater departure of researchers from the two-phase model, according to which there can exist only two physical states -the crystalline state (3D -long-range order) and the amorphous state (3D -near-range order).It is surprising how common the universally accepted viewpoint of the single-step fusion of a crystal as of the process typical of the condensed state of a substance has become. We consider the actual situation from a somewhat different viewpoint.The simplest crystals constructed from spherically shaped elements (for example, metals) are known to be characterized by the long-range position order in three independent dimensions. If the elements constituting the crystal lattice have an anisotropy of shape (rods or disks), orientation elements of order are added to the three position degrees of freedom. If such rods or disks have lateral substitutes, one should also take into account the rotation forms of ordering. Thus, the structural hierarchy of even a low-molecular-weight crystal can appear rather complex and can possess a rich combinatorics of different "degrees of freedom" or elements of order. As far as polymers whose macromolecules have a complex structure in themselves, possess a pronounced shape anisotropy, and are often characterized by cylindrical symmetry, here one should expect dramatic thermodynamic events "on the path from a crystal to a liquid."The question arises: from where does it follow that the entire rich hierarchy of order must be destroyed suddenly, simultaneously, at a single temperature point (and, needless to say, for a certain fixed value of pressure) in heating to form a totally "structureless" melt or, more precisely, a state characterized only by the near-range order in all three dimensions? It is much more natural to expect a step-by-step "melting" of some degrees of freedom or others in heating of the system, which means a multistep process of disordering, each step of which is separated from another by a phase transition of the first kind. This, in turn, points to the possibility of observing a sequence of polymorphic transformations of intermediate but simultaneously equilibrium structures in the temperature series (or on the pressure scale) with a gradual but discrete loss of the solid-state properties of a truly crystalline substance and approach to a truly liquid state. And that is the case. Each of such structures was considered first as an "exc...