We shall review some recent joint results concerning the Monster,the largest of the sporadic groups,involving 20 of the 26 sporadics.With Ching Hung Lam,we prove that there is a new and relatively easy construction involving vertex operator algebra representation theory.With Chongying Dong,we prove existence in certain vertex operator algebras of integral forms invariant by finite groups.This theory gives a Monster-invariant integral form in the Moonshine VOA.We shall look at examples and discuss theories underlying work with finite groups and VOAs.