A wide variety of quantum field and condensed phase phenomena arise as a result of the existence of particle-like excitations of continuous fields. In a liquid crystal model system, we have observed distinctive particle-like excitations in molecular orientation patterns that enable a continuous localized twist in 3D, which we call “toron”. The basic configuration is a double twist cylinder closed on itself in the form of a torus and coupled to a surrounding uniform field by a pair of point singularities, so that the topological charge is conserved. Remarkably, such structure enables significant localized molecular twist in all directions and can be incorporated into a uniform field. Numerical calculations show that this structure can be a ground state for confined chiral nematics. We also recently demonstrated that the torons are topologically equivalent to the much-storied Hopf fibration and that each toron can be transformed to it by annihilating topological point defects with each other. We continue to explore the stability, structural diversity, and possible new condensed matter phases formed by these and other “building blocks” with topological singularities.