Leibniz algebras are a generalization of Lie algebras. In this talk I will discuss some results on characteristic ideals, which are analogs of known results from Lie algebra. I will use these results to prove that the radical of a Leibniz algebra is a characteristic ideal. We will also explore the derivation algebra of cyclic Leibniz algebras broken down into two categories: the nilpotent case and the non nilpotent case. Upon observing the patterns in the derivation algebra of small examples, I will show the basis vectors for the derivation algebra of any n-dimensional cyclic Leibniz algebra.