Group theoretic hash functions are obtained by performing a walk in a Cayley graph. Since the first example by Zémor in 1991, it has been an active field of research. During my talk, discuss current existing platforms and attacks and speak about a joint work with Christopher Battarbee, Ramon Flores, Thomas Koberda and Delaram Kahrobaei. We have constructed hash functions using the groups SLn(Fp) as platforms. This gives many examples of group theoretic hash functions combining quick mixing properties and high girth, which give rise to good properties of hash functions. Finally, I will discuss possible developments on simplicial complexes of higher dimensions. This is joint work with Christopher Battarbee, Ramón Flores, Thomas Koberda and Delaram Kahrobaei.