Use of bacteriophage to control bacterial infections, including antibiotic-resistant infections, shows increasing therapeutic promise. Effective bacteriophage therapy requires awareness of various novel kinetic phenomena not known in conventional drug treatments. Kinetic theory predicts that timing of treatment could be critical, with the strange possibility that inoculations given too early could be less effective or fail completely. Another paradoxical result is that adjuvant use of an antibiotic can sometimes diminish the efficacy of phage therapy. For a simple kinetic model, mathematical formulae predict the values of critical density thresholds and critical time points, given as functions of independently measurable biological parameters. Understanding such formulae is important for interpreting data and guiding experimental design. Tailoring pharmacokinetic models for specific systems needs to become standard practice in future studies.