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This study examines the structure and stability of filamentary dusty plasmas using data from the Plasmakristall-4 (PK-4) facility on board the International Space Station. Under the action of a polarity-switched DC electric field, the dust particles in the PK-4 discharge have been found to organize into field-aligned extended filaments, which has been compared to the filamentary state in electrorheological (ER) fluids. Here we discuss how, in addition to an ER-type structural transition, the PK-4 dusty plasmas exhibit structural states reminiscent of those observed in liquid crystals (LCs) with rod-shaped molecules. We find that dust particles within the filaments are strongly coupled in a crystalline-like structure, while the coupling of particles across filaments is liquid-like. In addition to a common orientation along a director axis (nematic behavior), the dust filaments also appear to align in large-scale nested structures, or shells (smectic behavior). Finally, these filaments are found to further arrange in hexagonal patterns within the plane orthogonal to the director axis, suggesting the possibility for smectic-B and smectic-C structural states. As the observed ER and LC features of the filamentary dusty plasma states are sensitive to variations in the PK-4 discharge conditions, we argue that these dusty plasmas can provide a controlled analogous system for the study of fundamental phenomena in soft matter, such as the origins of pattern formation and universality of phase transitions.