This paper reviews some of our recent works on phase behaviors of particulate systems with a soft-core interaction potential. The potential is purely repulsive and bounded, i.e., it is finite even when two particles completely overlap. The one-sided linear spring (harmonic) potential is one of the representatives. This model system has been successively employed to study the jamming transition, i.e., the formation of rigid and disordered packings of hard particles, and establish the jamming physics. This is actually based on the hardaspect of the potential, because at low densities and when particle overlap is tiny the potential resembles the hard sphere limit. At high densities, the potential exhibits its soft aspect: with the increase of density, there are successive reentrant crystallizations with many types of solid phases. Taking advantage of the dual nature of the potential, we investigate the criticality of the jamming transition from different perspectives, extend the jamming scenario to high densities, reveal the novel density evolution of two-dimensional melting, and find unexpected formation of quasicrystals. It is surprising that such a simple potential can exhibit so rich and unexpected phenomena in phase transitions. The phase behaviors discussed in this paper are also highly regarded in polymer science, which may thus shed light on our understanding of polymeric systems or inspire new ideas in studies of polymers.