Structural plasticity and other forms of network remodeling are important and well-documented processes during brain development, maturation, learning, and aging. Remarkably high turnover rates in neural connectivity have been observed under baseline conditions, and these rates increase even more significantly in response to stimulation or perturbation. However, little is known about the underlying molecular mechanisms and biological function of this drastic form of brain plasticity. Since direct experiments on connectivity at the synaptic level are notoriously difficult to conduct and analyze, formal models are crucial for predicting and understanding the emergent properties of networks (or graphs) with highly dynamic structures. Building on our previous work on homeostatic structural plasticity, we have developed a new model of self-organizing networks based on the “directed configuration model.” It exhibits Hebbian plasticity (“neurons that fire together wire together”) and engram formation without specific molecular mechanisms. I will also discuss possible connections with psychological phenomena such as classical conditioning, extinction, and blocking, and describe new machine learning strategies based on self-organizing networks that can be derived from our biologically motivated theory.