Model pruning based on knowledge of the device equivalent circuit is proposed in this chapter to reduce the huge number of coefficients in a direct Volterra representation. First, model reduction techniques are accomplished by deepening into the nexus between the model parameters and the corresponding equivalent circuit of the power amplifier. Initially, a Volterra behavioral model for wideband amplifiers is demonstrated and possible equivalent circuits with additional subnetworks which reflect internal amplifier mechanisms are further considered. Internal mechanisms like the equivalent electrothermal or the charge-trapping subnetworks in transistors, and the envelope generation in envelope tracking power amplifiers, gives rise to a structure that is denoted bivariate CKV model. The popular GMP model can be considered a particular case of this bivariate CKV model. The complex Volterra model is also used here as a widely nonlinear approach to model IQ modulators and examine its impairments.