Topological states of matter is an umbrella term to designate phases of matter with 
very different physical origin, such as the Quantum Hall Effect (QHE), the topological insulators (TI) and the quantum spin liquids (QSL). Because of the differences, it is at first glance hard to see any relation between these states, giving the appearance that the branch of topological condensed mater theory is completely fragmented. In spite of that some connections were recently found between the QHE, TIs and QSLs, opening new guidances to look for models that support topological phases. In this seminar, such connections will be introduced. The focus will be on a correspondence between a modified Kitaev honeycomb model and the Haldane model and on 3D strongly correlated systems in the strong spin-orbit regime. The first case inspired the generation of tight-binding models that supports either a QSL or a TI phase, establishing a method of generating certain types of desired states. In the second case, we review the research into systems that have a combination of the key elements for the generation of topologically non-trivial phases.
