Dr. Stecker's body of research primarily concerns the application of particle physics to high energy astrophysics and also has included theoretical work on infrared astronomy and galactic structure. His research contributions include publishing the first book on gamma-ray astronomy, the calculation of galactic gamma-ray emission mechanisms and making the first detailed calculation of the cutoff of the ultrahigh energy cosmic ray spectrum owing to interactions with the cosmic background radiation (the GZK effect). In addition, he showed how gamma-ray astronomy could be used for galactic structure studies, showed that the observed diffuse galactic gamma-ray distribution implies a galactic origin for most cosmic rays and predicted generation mechanisms for and fluxes of galactic and extragalactic high energy neutrinos. His work has also involved calculating the spectra of secondary particles and gamma-rays from the annihilations of supersymmetric dark matter particles, predicting an observable flux of high energy neutrinos from the cores of active galaxies, showing how absorption features in high energy gamma-ray spectra of active galaxies could be used as a probe of the intergalactic infrared radiation and predicting extragalactic sources of TeV gamma-rays and their fluxes, calculating the extragalactic gamma-ray background from blazars and showing that blazars could account for most of the observed extragalactic gamma-ray background, calculating the spectral energy distribution of the extragalactic infrared background radiation and also showing that the highest energy cosmic ray events observed -- those beyond the "GZK cutoff" -- could be from partially photodisintegrated cosmic-ray nuclei.