This chapter offers a detailed exploration of control and stabilization approaches for fractional discrete-time memristor systems, focusing on their intricate nonlinear and memory-driven dynamics such as chaos, multistability, and hidden attractors. We present a variety of control methodologies, including state feedback, adaptive, active, and sliding mode techniques, specifically designed for fractional-order difference systems to regulate system behavior and suppress complex phenomena. Rigorous stability analyses are conducted using fractional Lyapunov methods, clarifying the impact of fractional order on system robustness. Through numerical simulations on representative fractional memristive models, we demonstrate the efficacy of these controllers in achieving stabilization and complexity reduction. Practical considerations for hardware implementation are discussed, and future research directions in the control of fractional-order nonlinear systems are outlined.