The Axiom of Limitation of Size is an axiom of set theory that states that a class is a proper class iff there is surjection from it to V, the set-theoretical universe.  But although it is an axiom that gained great attention in the beginnings of set theory,  nowadays it is no longer part of standard set theory,  not even of alternative axiomatizations such as NBG.  However, many  results  can  be  derived  from  it,  and  in  this work I will explain some of those that are already known, as well as stating new ones: that it implies that V=HOD, the existence of measurable cardinals, and the negation of the Axiom of Constructibility.  Equally, in the last section I will discuss the possibility of a set theoretical multiverse, as a solution for certain contradictions that can also be derived from the Axiom of Limitation of Size. For that, I will describe a possible picture of that multiverse.