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Neutron production with laser-driven neutron sources was demonstrated. We outline the basics of laser-driven neutron sources, highlight some fundamental advantages, and quantitatively compare the neutron production at the TRIDENT laser sources with the well-established LANSCE pulsed neutron spallation source. Ongoing efforts by our team to continue development of these sources, in particular the LANSCE-ina-box instrument, are described. The promise of ultra-intense lasers as drivers for brilliant, compact, and highly efficient particle accelerators portends driving next-generation neutron sources, potentially replacing in some cases much larger conventional accelerators. [ABSTRACT FROM AUTHOR]