CMOS technology and its continuous scaling have made electronics and computers accessible and affordable for almost everyone on the globe; in addition, they have enabled the solutions of a wide range of societal problems and applications. Today, however, both the technology and the computer architectures are facing severe challenges/walls making them incapable of providing the demanded computing power with tight constraints. This motivates the need for the exploration of novel architectures based on new device technologies; not only to sustain the financial benefit of technology scaling, but also to develop solutions for extremely demanding emerging applications. This paper presents two computation-in-memory based accelerators making use of emerging memristive devices; they are Memristive Vector Processor and RRAM Automata Processor. The preliminary results of these two accelerators show significant improvement in terms of latency, energy and area as compared to today's architectures and design.