Structural plasticity of dendritic spines underlies learning, memory and cognition in the cerebral cortex. We here summarize fifteen rules of spine structural plasticity, or ‘spine learning rules.’ Together, they suggest how the spontaneous generation, selection and strengthening (SGSS) of spines represents the physical basis for learning and memory. This SGSS mechanism is consistent with Hebb’s learning rule but suggests new relations between synaptic plasticity and memory. We describe the cellular and molecular bases of the spine learning rules, such as the persistence of spine structures and the fundamental role of actin, which polymerizes to form a ‘memory gel’ required for the selection and strengthening of spine synapses. We also discuss the possible link between transcriptional and translational regulation of structural plasticity. The SGSS mechanism and spine learning rules elucidate the integral nature of synaptic plasticity in neuronal network operations within the actual brain tissue.