Influenza causes annual global epidemics and severe morbidity and mortality. The influenza virus evolves to escape from immune system antibodies that bind to it. The immune system produces influenza virus specific antibodies by VDJ recombination and somatic hypermutation. In this dissertation, we analyze the mechanism of influenza virus evolution and immune system dynamics using theoretical modeling and computational simulation. The first half of this thesis discusses influenza virus evolution. The epidemiological data inspires a novel sequence-based antigenic distance measure for subtypes H1N1 and H3N2 virus, which are superior to the conventional measure using hemagglutination inhibition assay. Historical influenza sequences show that the selective pressure increases charge in immunodominant epitopes of the H3 hemagglutinin influenza protein. Statistical mechanics and high-performance computing technology predict fixation tendencies of the H3N2 influenza virus by free energy calculation. We introduce the notion of entropy from physics and informatics to identify the epitope regions of H1-subtype influenza A with application to vaccine efficacy. We also use entropy to quantify selection and diversity in viruses with application to the hemagglutinin of H3N2 influenza. Using the bacterial E. coli as a model, we show the evidence for recombination contributing to the evolution of extended spectrum β-lactamases (ES-BLs) in clinical isolates. A guinea pig experiment supports the discussion on influenza virus evolution. The second half of the thesis discusses immune system dynamics. We design a two-scale model to describe correlation in B cell VDJ usage of zebrafish. We also introduce a dynamical system to model original antigenic sin in influenza. This dissertation aims to help researchers understand the interaction between influenza virus and the immune system with a quantitative approach.