The emerging non-volatile memory technologies open novel perspectives for original highly-efficient and flexible architecture design. Dense integration of non-volatile memristors close to logic gates and circuit wires allows for new dimensions of reconfiguration and low power design. In this paper we present a review of the recent contributions that have investigated the use of memristors for different applications in digital design. Based on this review, and considering the widely used fast Fourier transform (FFT), we investigate for the first time a novel memristor-based reconfigurable FFT architecture. The proposed original architecture allows an efficient support of any combination of radix-2 and radix-3 butterflies. Scalability is ensured through a 2D mesh based topology and fast reconfiguration can be achieved using memristor-based interconnections.