With the advent of memristor-CMOS (MCM) process that combines CMOS processing with nano-scale memristive devices, it becomes possible to reduce utilization of silicon area thus providing a promising option in the design of MCM based circuits. Two properties of memristor have attracted the most attention. Firstly its nanometer scale dimensions and, secondly, its nonvolatile memory characteristics. The nanometer scale feature of the device creates a new opportunity for new logic elements allowing realization of innovative circuits that are removed from the more established design domains. The non-volatile memory property enables us to realize new design methods for a variety of computational elements that lead to novel architectures. In this paper, we present primitive logic blocks based on MCM design style those are also extended to special logic types like Domino logic and programmable logic array (PLA). We also provide an overview of modeling principles that would allow designers to venture into this new integrated domain.