In this survey paper, some new applications of $S$-unit equations are presented to certain arithmetic graphs and irreducible polynomials, to a conjecture on common polynomial divisors of trinomials, to families of solutions of decomposable form equations, to certain generalized systems of $S$-unit equations, and to binary forms and decomposable forms of given discriminant. Further, some consequences of a generalization of Baker's type inequalities are discussed for $S$-unit equations.