This talk builds on Eran Nevo's talk, where he presented results and problems on f-vectors of simplicial complexes and polytopes. We will provide an overview of some of the most important tools used to prove this kind of results. This includes combinatorial methods such as shellings, as well as algebraic and geometric methods such as Stanley-Reisner rings, sigma modules, toric varieties, Lefschetz properties and rigidity of frameworks. We will also hint at specific examples, where those techniques have been applied successfully.