This thesis investigates some properties of complex structures on Lie algebras. In particular, we focus on nilpotent complex structures that are characterized by a suitable J-invariant ascending or descending central series dj and dj respectively. In this thesis, we introduce a new descending series pj and use it to give proof of a new characterization of nilpotent complex structures. We examine also whether nilpotent complex structures on stratified Lie algebras preserve the strata. We find that there exists a J-invariant stratification on a step 2 nilpotent Lie algebra with a complex structure.