It is possible to obtain information about various properties of the fuel ions deuterium (D) and tritium (T) in a fusion plasma by measuring the neutron emission from the plasma. Neutrons are produced in fusion reactions between the fuel ions, which means that the intensity and energy spectrum of the emitted neutrons are related to the densities and velocity distributions of these ions. This thesis describes different methods for analyzing data from fusion neutron measurements. The main focus is on neutron spectrometry measurements, using data used collected at the tokamak fusion reactor JET in England. Several neutron spectrometers are installed at JET, including the time-of-flight spectrometer TOFOR and the magnetic proton recoil (MPRu) spectrometer. Part of the work is concerned with the calculation of neutron spectra from given fuel ion distributions. Most fusion reactions of interest – such as the D + T and D + D reactions – have two particles in the final state, but there are also examples where three particles are produced, e.g. in the T + T reaction. Both two- and three-body reactions are considered in this thesis. A method for including the finite Larmor radii of the fuel ions in the spectrum calculation is also developed. This effect was seen to significantly affect the shape of the measured TOFOR spectrum for a plasma scenario utilizing ion cyclotron resonance heating (ICRH) in combination with neutral beam injection (NBI). Using the capability to calculate neutron spectra, it is possible to set up different parametric models of the neutron emission for various plasma scenarios. In this thesis, such models are used to estimate the fuel ion density in NBI heated plasmas and the fast D distribution in plasmas with ICRH.