The idea that multiplication of virulent phage depends on its host's physiological state, conceived by Delbrück in the 1940' s, was extended. The kinetic parameters, at least in the T4/Escherichia coli system, are related solely to the bacterial growth rate. Numerical models were advanced to explain (a) the co-existence of bacteriophage and its susceptible bacteria based on phage 'suicidal' phenomenon, (b) the kinetics of cell lysis based on materials corrosion, statistics of extremes and knowledge on bacterial and phage biology, and (c) to maximize phage titers in exponentially growing cultures. The hybrid model for the latter consists of probabilistic and delayed differential equations. Results display a range of possible values for bacterial doubling time and multiplicity of infection along a "golden strip" in the relevant plane, and times to achieve these maxima and gains in phage concentrations are evaluated. High resolution of the adsorption kinetics found fast drop in free phage and bacteria, consistent with a simple model. The sharper reduction in viable cells indicates that adsorption is a more complex process than thought to be. The models are consistent with experimental results hence support predictability and potential use to improve Phage Therapy. We do not pretend to exhaust the studies extended over a Century, but summarize 2 decades of research at Ben-Gurion University.