Strongly correlated systems provide a fertile ground for discovering exotic states of matter, for example, those with topologically non-trivial properties. Among these are frustrated magnets, where the lattice geometry prevents spins from ordering even at very low temperatures, thereby leading to exotic phases. I will present two of our works in this area, both focusing on the kagome geometry which has near-ideal realizations in several materials. First, I present a study of the spin-1 Heisenberg antiferromagnet, where contrary to previous theoretical proposals, our calculations indicate that the ground state is a valence bond (simplex) solid with a spin gap that is consistent with experimental findings . In the second part of the talk, motivated by the discovery of a spin liquid in herbertsmithite, I revisit aspects of the spin-1/2 XXZ model on the kagome lattice whose complete understanding still baffles the community. After briefly presenting evidence for the existence of a "chiral spin liquid" in a magnetic field , I primarily focus on our recent finding of a special (and previously missed) point on the phase diagram where exact three coloring ground states exist . I conclude by discussing the impact of the presence of this special point on the general phase diagram of the spin 1/2 kagome antiferromagnet.
 H.J. Changlani, A. M. Lauchli, Phys. Rev. B 91, 100407(R) (2015).
 K. Kumar, H. J. Changlani, B. Clark, E. Fradkin, Phys. Rev. B 94, 134410 (2016).
 H. J. Changlani, D. Kochkov, K. Kumar, E. Fradkin, B. Clark (in preparation, 2017).