Systems of strongly interacting particles can give rise to topological phases that are not accessible to non-interacting systems. Although unique features of strongly interacting topological phases, such as fractionalization of quantum degrees of freedom, have important applications in quantum information processing, they are still far from experimental realizations. In this talk, by presenting constructions of two strongly interacting topological phases, I will argue the key mechanism of their realizations is to add interactions near topological phase transitions. I will first introduce a model of interacting Majorana fermions that describes a superconducting phase with Fibonacci topological order. Then I will show that a correlated fluid of electrons and holes, dubbed fractional excitonic insulator phase, can exhibit a fractional quantum Hall effect at zero magnetic field. I will present physical evidence and conjecture that this phase can be realized in a higher angular momentum excitonic paired system in the presence of interactions.