Fast neutron therapy is a high linear energy transfer (LET) radiation treatment modality offering advantages over low LET radiations. Multileaf collimator technology reduces normal-tissue dose (toxicity) and makes neutron therapy more comparable to MV x-ray treatments. Published clinical-trial and other experiences with fast neutron therapy are reported. Early comparative studies failed to consider differences in target-dose spatial conformality between x-ray and neutron treatments, which is especially important for organs-at-risk close to tumor targets. Treatments planning systems (TPS) for high-energy neutrons lag behind TPS tools for MV x-rays, creating challenges for comparative studies of clinical outcomes. A previously published Monte Carlo model of the University of Washington (UW) Clinical Neutron Therapy System (CNTS) is refined and integrated with the RayStation TPS as an external dose planning/verification tool. The collapsed cone (CC) dose calculations in the TPS are based on measured dose profiles and output factors in water, with the absolute dose determined using a tissue-equivalent ionization chamber. For comparison, independent (external) Monte Carlo simulation computes dose on a voxel-by-voxel basis using an atlas that maps Hounsfield Unit (HU) numbers to elemental composition and density. Although the CC algorithm in the TPS accurately computes neutron dose to water compared to Monte Carlo calculations, calculated dose to water differs from bone or tissue depending largely on hydrogen content. Therefore, the elemental composition of tissue and bone, rather than the material or electron density, affects fast neutron dose. While the CC algorithm suffices for reproducible patient dosimetry in fast neutron therapy, adopting methods that consider tissue heterogeneity would enhance patient-specific neutron dose accuracy relative to national standards for other types of ionizing radiation. Corrections for tissue composition have a significant impact on absolute dose and the relative biological effectiveness (RBE) of neutron treatments compared to other radiation types (MV x-rays, protons, and carbon ions).