A gas dynamic trap (GDT) is a version of a magnetic mirror whose characteristic features are a long mirror-to-mirror distance, which exceeds the effective mean free path of ion scattering into a loss cone, a large mirror ratio (R similar to 100) and axial symmetry. Under these conditions, the plasma confined in a GDT is isotropic and Maxwellian. The rate at which it is lost out of the ends is governed by a set of simple gas-dynamic equations, hence the name of the device. Plasma magnetohydrodynamic stability is achieved through a plasma outflow through the end mirrors into regions, where the magnetic-field lines' curvature is favorable for this stability. A high flux volumetric neutron source based on a GDT is proposed, which benefits from the high beta achievable in magnetic mirrors. Axial symmetry also makes the GDT neutron source more maintainable and reliable, and technically simpler. This review discusses the results of a conceptual design of the GDT-based neutron source for fusion materials development and fission-fusion hybrids. The main physics issues related to plasma confinement and heating in a GDT are addressed by the experiments performed with the GDT device in Novosibirsk. The review concludes by updating the experimental results obtained, a discussion about the limiting factors in the current experiments and a brief description of the design of a future experimental device for more comprehensive modeling of the GDT-based neutron source.