A roadmap is suggested and demonstrated experimentally for the production of high-energy (>15 MeV) neutrons using short pulse lasers. Investigation with a 3D Monte Carlo model has been employed to quantify the production of energetic neutrons. Numerical simulations have been performed for three nuclear reactions, d(d,n)3He, 7Li(d,n)8Be, and 7Li(p,n)7Be, driven by monoenergetic ion beams. Quantitative estimates for the driver ion beam energy and number have been made and the neutron spectra and yield in the ion propagation direction have been evaluated for various incident ion energies. In order to generate neutron fluence above a detection limit of 106 neutrons/sr, either ∼1010 protons with energy 20–30 MeV or comparable amount of deuterons with energy 5–10 MeV are required. Experimental verification of the concept with deuterons driven by the Titan laser (peak intensity 2 × 1019 W/cm2, pulse duration of 9 ps, wavelength 1.05 μm, and energy of 360 J) is provided with the generation of neutrons with energy of up to 18 MeV from 7Li(d,n)8Be reactions. Future research will focus on optimized schemes for ion acceleration for production of high-energy neutrons, which will involve efficient target design, laser parameter optimization, and converter material.