The code couples the electrical circuit with plasma focus (PF) dynamics, thermodynamics and radiation. It is energy-, charge- and mass-consistent and accounts for the effects of transit times of small disturbances and plasma self-absorption. It has been used in design and interpretation of Mather-type PF experiments and as a complementary facility to provide diagnostic reference numbers in all gases. Information computed includes axial and radial dynamics, SXR emission characteristics and yield for various applications including microelectronics lithography and optimization of machines. Plasma focus neutron yield calculations, current and neutron yield limitations, deterioration of neutron scaling (neutron saturation), radiative collapse, speed-enhanced PF, current-stepped PF and extraction of diagnostic and anomalous resistance data from current signals have been studied using the code; which also produces reference numbers for fluence, flux and energy of deuteron beams and ion beams for all gases. There has been no pause in its continuous evolution in three decades so much so that the model code has no formal source reference except www.plasmafocus.net . This review presents, for the first time a comprehensive up-to-date version of the 5-phase model code. The equations of each phase are derived. Those of the first two phases are normalized to reveal important scaling parameters. The focus pinch phase is discussed with radiation-coupled dynamics necessitating the computation of radiation terms moderated by plasma self-absorption. Neutron and ion beam yields are computed. The 5-phase model code appears to be adequate for all Mather-type PF, lacking only in one aspect that for high inductance PF (termed Type 2) the measured current waveform contains an extended dip which cannot be fitted by the 5-phase code; necessitating an extended 6-phase code. This sixth phase (termed phase 4a) is dominated by anomalous resistance, providing a way to extract valuable data on anomalous resistivity from the current trace.