Liquid crystals (LCs) are elastic fluids consisting of anisotropic molecules that exhibit orientational ordering, aligning along an average direction—the director n. Optically, LCs are uniaxial crystals with an optical axis parallel to n. Together with their elastic properties, these aspects make LCs useful for many technological applications and for studying fundamental phenomena generally common to a broad range of physical systems, i.e. electric and magnetic fields, atomic systems and superfluid vortices. Other soft condensed matter systems, such as polymers and colloids, also exhibit interesting entropic and elastic properties that govern the dynamics and symmetry of their self-organization. In this talk, I will discuss my work with composite materials that combine these soft matter systems, exploring ways to shape their symmetry and topology and to and guide their self-organization to discover new potential applications and study concepts in fundamental physics and mathematics that are difficult to study in other physical systems.