Properties of neural circuits are demonstrated via SPICE simulations and their applications are discussed. The neuron and synapse subcircuits include ambipolar nano-crystalline silicon transistor and memristor device models based on measured data. Neuron circuit characteristics and the Hebbian synaptic learning rule are shown to be similar to biology. Changes in the average firing rate learning rule depending on various circuit parameters are also presented. The subcircuits are then connected into larger neural networks that demonstrate fundamental properties including associative learning and pulse coincidence detection. Learned extraction of a fundamental frequency component from noisy inputs is demonstrated. It is then shown that if the fundamental sinusoid of one neuron input is out of phase with the rest, its synaptic connection changes differently than the others. Such behavior indicates that the system can learn to detect which signals are important in the general population, and that there is a spike-timing-dependent component of the learning mechanism. Finally, future circuit design and considerations are discussed, including requirements for the memristive device.