In recent years, space-borne experiments have delivered new measurements of high energy cosmic ray (CR) antiprotons and positrons. We report on the theoretical interpretation of these measurements, presenting evidence that CR antiprotons and positrons most likely come from astrophysical secondary production and do not require exotic contributions from, e.g., dark matter or pulsars. In addition, based on recent accelerator analyses we show that the flux of secondary anti-deuterons and anti-helions may be observable with the AMS-02 experiment.