This thesis develops adaptive reduction approaches for various models of large spiking neurons. Most neurons are like dendritic trees with many branches, and they communicate by nonlinear spiking behaviors. However, with the exception of Kellems' Strong-Weak model, most existing reduction approaches compromise the active ionic mechanisms that cause the spiking dynamics. The Strong-Weak model can predict the spikes caused by suprathreshold input traveling from the dendritic branches to the spike initiation zone (SIZ), but it is not able to reproduce the back propagation from SIZ to the dendritic branches after spikes. This thesis develops a new model called QAact, the mechanisms to incorporate QAact into the hybrid model to capture the back propagation behavior, and different model reduction techniques for each part of the new hybrid model where they are most advantageous. Computational tests of QAact and the new hybrid model as well as corresponding model reduction techniques on FitzHugh-Nagumo system, active nonuniform cable, and branched cell LGMD, demonstrate a significant reduction of dimension, computational complexity and running time.