This paper investigates the reproducibility of computational science research and identifies key challenges facing the community today. It is the result of the First Summer School on Experimental Methodology in Computational Science Research (this https URL). First, we consider how to reproduce experiments that involve human subjects, and in particular how to deal with different ethics requirements at different institutions. Second, we look at whether parallel and distributed computational experiments are more or less reproducible than serial ones. Third, we consider reproducible computational experiments from fields outside computer science. Our final case study looks at whether reproducibility for one researcher is the same as for another, by having an author attempt to have others reproduce their own, reproducible, paper. This paper is open, executable and reproducible: the whole process of writing this paper is captured in the source control repository hosting both the source of the paper, supplementary codes and data; we are providing setup for several experiments on which we were working; finally, we try to describe what we have achieved during the week of the school in a way that others may reproduce (and hopefully improve) our experiments.