Biological neurons can perceive a variety of physical and chemical signals and appropriate firing modes can be induced to maintain suitable energy levels accompanying with right firing patterns. Physical and chemical stimuli including current, electromagnetic field, acoustic wave, illumination, and odor can be converted into equivalent currents on the cell membrane or ion channels. Memristive terms enable the sensor ability of electromagnetic induction in biophysical neurons by introducing memristive current and variables including charge and magnetic flux. The activation of memristive synapses can enhance the controllability and multistability of memristive neurons, and then energy diversity supports adaptive control in intrinsic parameters and mode selection in neural activities. These functional neurons can be clustered to develop functional neural networks and gradient energy diversity and local energy balance support formation of defects and heterogeneity, which control the wave propagation and synchronization stability of neural networks. This special issue summarizes new achievements about physical descriptions in functional biophysical neurons and networks, and functional enhancement of neuron models and neural circuits, wave propagation in neural networks. This SI has collected 67 papers, and these results in this special issue have potential application in control of electromechanical arms and computational neuroscience for further prevention of nervous diseases.