Contrary to abundant memory related studies of memristive crossbar structures, logic oriented applications are only gaining popularity in recent years. In this paper, we study logic synthesis, regarding both two-level and multi level designs, and defect aspects of memristor based crossbar architectures. First, we introduce our two-level and multi-level logic synthesis techniques. We elaborate on advantages and disadvantages of both approaches with experimental results regarding area cost. After that, we devise a defect model in alignment with the conventional stuck-at open and closed paradigm. In addition, we determine the effects of defects to the operational capacity of the crossbar. Furthermore, we propose a preliminary defect tolerant. Boolean logic mapping approach. In order to evaluate our approach, we conduct extensive Monte Carlo simulations with industrial benchmarks. Finally, we discuss future directions concerning both existing two-level and prospective multi-level logic designs as well as defect tolerance with area redundancy.