This talk will review the basic physical and computational characteristics of neutron transport problems for nuclear reactor cores (and coupled neutron-photon transport for nuclear reactor shields). The underlying physical nature of these problems (in terms of how they differ from other types of particle transport problems) will be outlined, and the basic computational methods that have been developed during the past 50 years for solving these problems will be characterized. The talk will include a discussion of some current popular research topics and significant open problems. The overall goal of the talk is to introduce the audience to the types of neutron and photon transport problems in the practical arena of nuclear engineering, and the types of computational methods that currently exist and are on the drawing board for solving these problems.