This paper reviews the development of low-energy light ion accelerator-based neutron sources (ABNSs) for the treatment of brain tumors through an intact scalp and skull using boron neutron capture therapy (BNCT). A major advantage of an ABNS for BNCT over reactor-based neutron sources is the potential for siting within a hospital. Consequently, light-ion accelerators that are injectors to larger machines in high-energy physics facilities are not considered. An ABNS for BNCT is composed of: (1) the accelerator hardware for producing a high current charged particle beam, (2) an appropriate neutron-producing target and target heat removal system (HRS), and (3) a moderator/reflector assembly to render the flux energy spectrum of neutrons produced in the target suitable for patient irradiation. As a consequence of the efforts of researchers throughout the world, progress has been made on the design, manufacture, and testing of these three major components. Although an ABNS facility has not yet been built that has optimally assembled these three components, the feasibility of clinically useful ABNSs has been clearly established. Both electrostatic and radio frequency linear accelerators of reasonable cost (approximately 1.5 M dollars) appear to be capable of producing charged particle beams, with combinations of accelerated particle energy (a few MeV) and beam currents (approximately 10 mA) that are suitable for a hospital-based ABNS for BNCT. The specific accelerator performance requirements depend upon the charged particle reaction by which neutrons are produced in the target and the clinical requirements for neutron field quality and intensity. The accelerator performance requirements are more demanding for beryllium than for lithium as a target. However, beryllium targets are more easily cooled. The accelerator performance requirements are also more demanding for greater neutron field quality and intensity. Target HRSs that are based on submerged-jet impingement and the use of microchannels have emerged as viable target cooling options. Neutron fields for reactor-based neutron sources provide an obvious basis of comparison for ABNS field quality. This paper compares Monte Carlo calculations of neutron field quality for an ABNS and an idealized standard reactor neutron field (ISRNF). The comparison shows that with lithium as a target, an ABNS can create a neutron field with a field quality that is significantly better (by a factor of approximately 1.2, as judged by the relative biological effectiveness (RBE)-dose that can be delivered to a tumor at a depth of 6cm) than that for the ISRNF. Also, for a beam current of 10 mA, the treatment time is calculated to be reasonable (approximately 30 min) for the boron concentrations that have been assumed.