This paper presents an overview of the latest developments in the designing of low-enriched uranium nuclear thermal rockets (LEU-NTR). The concept is first introduced and explained in the context of human exploration of Mars and the development time frames associated with current and future research. The need for LEU fuel is established and the process by which LEU fuel is introduced is described. The importance of the moderator to fuel ratio is explained and the size limitations associated with the cooling requirements of the core are detailed. Once the general performance and neutronic requirements have been established, a series of design issues are identified including current trends for their successful resolution. These include the minimization of active reactivity control in reactor operation and the resolution of the full-submersion criticality accident. The implementation of spectral shift absorbers, rapid depletion neutron poisons, specialized axial and radial reflectors, and enhanced core hydrogen worth are briefly explored and compared. Following this overview of limitations and design requirements for LEU-NTRs, the possibility for different thrust levels is explored. Here, a comparison of two thrust classes is provided along with a development of requirements that govern the minimum core size for each thrust class.