The National Space Science Data Center (NSSDC) trapped radiation models calculate the integral and differential electron and proton flux for given values of particle energy E, drift shell parameter L, and magnetic field strength normalized to the equatorial/minimum value on the field line B/B0 for either solar maximum or solar minimum conditions. The most recent versions of the series of models, which have been developed and continuously improved over several decades by Vette and co-workers at NSSDC, are AE-8 for electrons and AP-8 for protons. The paper provides a brief history of the modeling efforts at NSSDC and discusses some of the problems encountered when applying the models at low altitudes. Recommendations are made and discussed about the correct use of the trapped particle models in conjunction with geomagnetic field models. Specifically, the importance of using the correct dipole moment and the correct B0 value (i.e., obtained by field line tracing) is illustrated.