<p>Investigating the neutron spectra produced by thermonuclear fusion reactions <i>D(d</i>,<i> n)</i>^<i>3</i><i>He</i> and <i>T(d</i>,<i> n)</i>^<i>4</i><i>He</i>, which will power the future fusion reactors, is a critical factor in improving the performance of fusion reactors. Experimentally, it is extremely difficult to measure the neutron spectrum of each fusion reaction independently and simultaneously. Hence, accurate theoretical calculations of the fusion neutron spectra are required. Monte Carlo technique is the ideal method for achieving such calculations. In classical physics, initiating the fusion of hydrogen isotope ions requires energy to overcome the Coulomb repulsion (at least 100&#xa0;keV/ion). However, the quantum tunneling effect allows thermonuclear fusion of hydrogen isotopes to occur at energies around 1.0&#xa0;keV. Future fusion reactors will operate at temperatures ranging from 100 to 150&#xa0;million kelvin (≈ 8.6–12.9&#xa0;keV). After comparing a set of Monte Carlo codes commonly used to simulate nuclear fusion, it was found that the MCUNED code can reproduce the experimentally measured neutron spectrum of the D-D thermonuclear fusion at approximately 1.0&#xa0;keV. It also predicts the D-T thermonuclear fusion spectrum resulting from inertial confinement fusion (ICF). Also, analytical models that don’t require approximations in their derivation can calculate fusion neutron spectra from D-D and D-T thermonuclear fusion.</p>