Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Several research groups have developed techniques independently to achieve this goal. While these methods have all provided remarkably high-precision mass maps, particularly with exquisite imaging data from the Hubble Space Telescope (HST), the reconstructions themselves have never been directly compared. In this paper, we present for the first time a detailed comparison of methodologies for fidelity, accuracy and precision. For this collaborative exercise, the lens modelling community was provided simulated cluster images that mimic the depth and resolution of the ongoing HST Frontier Fields. The results of the submitted reconstructions with the un-blinded true mass profile of these two clusters are presented here. Parametric, free-form and hybrid techniques have been deployed by the participating groups and we detail the strengths and trade-offs in accuracy and systematics that arise for each methodology. We note in conclusion that several properties of the lensing clusters are recovered equally well by most of the lensing techniques compared in this study. For example, the reconstruction of azimuthally averaged density and mass profiles by both parametric and free-form methods matches the input models at the level of similar to 10 per cent. Parametric techniques are generally better at recovering the 2D maps of the convergence and of the magnification. For the best-performing algorithms, the accuracy in the magnification estimate is similar to 10 per cent at mu(true) = 3 and it degrades to similar to 30 per cent at mu(true) similar to 10.