Physarum polycephalum’s foraging has been for a long time a real source of inspiration for scientists and researchers as it exhibits intrinsic optimization characteristics. When some sources of nutrients are present, Physarum connects these sources with its protoplasmic vascular network, along shortest path connections. This chapter presents the modeling of Physarum’s learning and adaptivity to periodic environmental changes by a memristor-based passive LC filter, and further demonstrates its computational capabilities through two different electronic approaches. Firstly, a circuit-level model of Physarum’s oscillatory internal motion mechanism is designed to emulate the local signal propagation and the expansion of its vascular network during biological shortest path finding experiments. Furthermore, an extension of this model in a system-level approach is presented, which introduces also the shrinking mechanism that Physarum performs to reduce its power consumption after it has reached every nutrient source within its environment. The proper functioning of both the aforementioned approaches was verified via circuit simulations in SPICE as well as MATLAB. Finally, the effect of environmental noise was integrated to the presented approaches, permitting their evaluation under more realistic circumstances closer to the biological experiments, with very interesting results.