  In recent years, breakthroughs in methods and data have enabled gravitational
time delays to emerge as a very powerful tool to measure the Hubble constant
$H_0$. However, published state-of-the-art analyses require of order 1 year of
expert investigator time and up to a million hours of computing time per
system. Furthermore, as precision improves, it is crucial to identify and
mitigate systematic uncertainties. With this time delay lens modelling
challenge we aim to assess the level of precision and accuracy of the modelling
techniques that are currently fast enough to handle of order 50 lenses, via the
blind analysis of simulated datasets. The results in Rung 1 and Rung 2 show
that methods that use only the point source positions tend to have lower
precision ($10 - 20\%$) while remaining accurate. In Rung 2, the methods that
exploit the full information of the imaging and kinematic datasets can recover
$H_0$ within the target accuracy ($ |A| < 2\%$) and precision ($< 6\%$ per
system), even in the presence of poorly known point spread function and complex
source morphology. A post-unblinding analysis of Rung 3 showed the numerical
precision of the ray-traced cosmological simulations to be insufficient to test
lens modelling methodology at the percent level, making the results difficult
to interpret. A new challenge with improved simulations is needed to make
further progress in the investigation of systematic uncertainties. For
completeness, we present the Rung 3 results in an appendix, and use them to
discuss various approaches to mitigating against similar subtle data generation
effects in future blind challenges.
