Despite the widespread emergence of memory effects in solid systems, understanding the basic microscopic mechanisms that trigger them is still puzzling. We report how ingredients of solid state transport in polycrystalline systems, such as semiconductor oxides, become sufficient conditions for a memristive response that points to the natural emergence of memory, discernible under an adequate set of driving inputs. The experimental confirmation of these trends will be presented along with a compact analytical theoretical picture that allows discerning the relative contribution of the main building blocks of memory and the effect of temperature, in particular. These findings can be extended to a vast universe of materials and devices, providing a unified physical explanation for a wide class of resistive memories and pinpointing the optimal driving configurations for their operation.