Polymer self-assembly has become a reliable and versatile workhorse to produce polymeric nanomaterials. With appropriate polymer design and monomer selection, polymers can assemble into shapes and morphologies beyond well-studied spherical and cylindrical micellar structures. Steadfast access to anisotropic polymer nanoparticles has meant that the fabrication and application of 2D soft matter has received increasing attention in recent years. In this review, we focus on nanoscale polymer discs, toroids, and platelets: three morphologies that are often interrelated and made from similar starting materials or common intermediates. For each morphology, we illustrate design rules, and group and discuss commonly used self-assembly strategies. We further highlight polymer compositions, fundamental principles and self-assembly conditions that enable precision in bottom-up fabrication strategies. Finally, we summarise potential applications of such nanomaterials, especially in the context of biomedical research and template chemistry and elaborate on future endeavours in this space.