Our paper deals with the classification of abstract regular polytopes for almost simple groups with socle PSL(2,q). We consider all almost simple groups PSL(2,q)≤G≤PΓL(2,q) and determine the maximal rank of string C-group representations for G, i.e. the maximal rank of an abstract regular polytope with automorphism group G, as well as the existence of string C-group representations of lower ranks. Similar results have already been obtained by various authors in the cases G≅PSL(2,q) and G≅PGL(2,q) and they are summarized in this paper.