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Memristors show great potential for being integrated into CMOS technology and provide new approaches for designing computing-in-memory (CIM) systems, brain-inspired applications, trimming circuits and other topologies for the beyond-CMOS era. A crucial characteristic of the memristor is multi-state (also often referred as multibit, and multi-level) switching. Memristors are capable of representing information in an ultra-compact fashion, by storing multiple bits per device. However, certain challenges remain in multi-state memristive circuits and systems design such as device stability and peripheral circuit complexity. In this paper, we review the state of the art of multi-state memristor technologies and their associated CMOS/Memristor circuit design, and discuss the challenges regarding device imperfection factors, modelling, peripheral circuit design and layout. We present measurement results of our in-house …