Even though simulating strongly correlated systems remains a challenge, the condensed matter physics community has made significant recent advances in this area. My talk will focus on tensor network methods (in particular the density matrix renormalization group (DMRG)), which have helped develop our understanding of quantum systems in low dimensions. In addition to providing reliable numerical simulation tools, these methods have highlighted the importance of analysing reduced density matrices. This in turn has provided a unifying language to characterize a wide variety of systems. In the first part of my talk, I will present aspects of DMRG in the context of our work on the spin-1 kagome lattice antiferromagnet, a system which several experimental groups have realized. In the second part of the talk, I will discuss our recent efforts to devise novel ways for using reduced density matrices to understand strongly correlated systems.