Abstract: Understanding the electrical mechanisms underlying artificial synaptic plasticity is essential for neuromorphic engineering. This work presents a unified electrical perspective connecting the simple bioelectrochemical dendrites and the greater complexity of memristors as complementary platforms for studying memory effects in artificial brain-inspired synapses. First, we show how conducting polymer dendrites exhibit fractional-order transient responses arising from coupled ionic and electrochemical proce sses, reproducing key features of synaptic plasticity such as history-dependent dynamics and synaptic learning behavior during morphogenesis. Similar electrical signatures are observed in halide perovskite memristors, where ion migration and charge accum ulation govern conductance modulation and short-/long-term potentiation. By combining Impedance Spectroscopy and transient analysis, we explain the electrical tools for quantifying the physics-based memory effects across biology and neuromorphic engineer ing. This electrical approach bridges bioelectrochemistry and neuromorphic hardware, offering new insights into the physical origins of synaptic functionality while providing practical guidance for the design and interpretation of next-generation brain-i nspired electronic systems.