One of the most profound mysteries in modern cosmology is the accelerated expansion of the universe (the discovery of which led to the 2011 physics Nobel Prize). Weak gravitational lensing, an observational method that has the potential to shed the most light on this mystery, relies on accurate measurement of the shapes of millions of galaxies to uncover tiny distortions caused by matter between the galaxies and us. However, accurately inferring the true galaxy shapes is complicated due to large distortions from the atmosphere, telescope optics, detector and pixel noise. As data arrives in greater quantities, requirements on measurement accuracy become more stringent, and weak lensing must now meet unprecedented image analysis challenges. This need has driven ongoing improvements to shape measurement algorithms, and led to the creation of public data analysis challenges, of which the STEP1, STEP2, GREAT08 and GREAT10 challenges are recent examples. Some approaches have been successfully honed and tested by astronomers, but winning entrants have also been found from the machine learning community. In this poster we summarize what has been learned about shape measurement systematics from previous challenges, and highlight critical issues for the field in the near future, which will be tested in the next weak lensing data challenge (currently under development).