Antimicrobial peptides (AMPs) are naturally-occurring molecules that exhibit strong antibiotic properties against numerous infectious bacterial strains. Because of their unique mechanism of action, they have been touted as a potential source for novel antibiotic drugs. We present a summary of computational investigations in our lab aimed at understanding this unique mechanism of action, in particular the development of models that provide a quantitative connection between molecular-level biophysical phenomena and relevant biological effects. Our work is focused on protegrins, a potent class of AMPs that attack bacteria by associating with the bacterial membrane and forming transmembrane pores that facilitate the unrestricted transport of ions. Using fully atomistic molecular dynamics simulations, we have computed the thermodynamics of peptide-membrane association and insertion, as well as peptide aggregation. We also present a multi-scale analysis of the ion transport properties of protegrin pores, ranging from atomistic molecular dynamics simulations to mesoscale continuum models of single-pore electrodiffusion to models of transient ion transport from bacterial cells. Overall, this work provides a quantitative mechanistic description of the mechanism of action of protegrin antimicrobial peptides across multiple length and time scales.