For interpreting fusion rate measurements in present fusion experiments and predicting the fusion performance of future devices or of d-t experiments in present devices, it is important to know the fusion cross-sections as precisely as possible. Usually, it is not measured data that are used, but parametrizations of the cross-section as a function of the ion energy and parametrizations of the Maxwellian reactivity as a function of the ion-temperature. Since the publication of the parametrizations now in use, new measurements have been made and evaluations of the measured data have been improved by applying R-matrix theory. The authors show that the old parametrizations no longer adequately represent the experimental data and present new parametrizations based on R-matrix calculations for fusion cross-sections and Maxwellian reactivities for the reactions D(d,n)3He, D(d,p)T, T(d,n)4He and 3He(d,p)4He