Nanoscale components often exhibit memory, both quantum and classical. Resistors are no exception (already at the classical level) and the use of memristors for a variety of purposes is currently under scrutiny. Applications range from machine learning on chip to compact and passive memory devices using crossbar arrays. In this talk we discuss the nitty-gritty mathematical aspects of memristive circuits in the analog regime (no CMOS), their connection to the Ising model, and plausible future directions beyond crossbars.