Galactic cosmic rays, which are thought to be produced and accelerated by a variety of mechanisms in the Milky Way galaxy, interact with the solar wind, the earth's magnetic field, and its atmosphere to produce hadron, lepton, and photon fields at aircraft altitudes that are quite unlike anything produced in the laboratory. The energy spectra of these secondary particles extend from the lowest possible energy to energies over an EeV. In addition to cosmic rays, energetic particles, generated on the sun by solar flares or coronal mass ejections, bombard the earth from time to time. These particles, while less energetic than cosmic rays, also produce radiation fields at aircraft altitudes which have qualitatively the same properties as cosmic rays. The authors have calculated atmospheric cosmic-ray angular fluxes, spectra, scalar fluxes, and ionization, and compared them with experimental data. Agreement with these data is seen to be good. These data have been used to calculate equivalent doses in a simplified human phantom at aircraft altitudes and the estimated health risks to aircraft crews. The authors have also calculated the radiation doses from several large solar energetic particle events (known as GLEs, or Ground Level Events), which took place in 1989, including the very large event known as GLE 42, which took place on September 29th and 30th of that year. The spectra incident on the atmosphere were determined assuming diffusive shock theory. Unfortunately, there are essentially no experimental data with which to compare these calculations.