The measurement of a quantity is reproducible when mutually independent, multiple measurements made of it yield mutually consistent measurement results, that is, when the measured values, after due allowance for their associated uncertainties, do not differ significantly from one another. Interlaboratory comparisons organized deliberately for the purpose, and meta analyses that are structured so as to be fit for the same purpose, are procedures of choice to ascertain measurement reproducibility. The realistic evaluation of measurement uncertainty is a key preliminary to the assessment of reproducibility because lack of reproducibility manifests itself as dispersion or variability of measured values in excess of what their associated uncertainties suggest that they should exhibit. For this reason, we review the distinctive traits of measurement in the physical sciences and technologies, including medicine, and discuss the meaning and expression of measurement uncertainty. This contribution illustrates the application of statistical models and methods to quantify measurement uncertainty and to assess reproducibility in four concrete, real-life examples, in the process revealing that lack of reproducibility can be a consequence of one or more of the following: intrinsic differences between laboratories making measurements; choice of statistical model and of procedure for data reduction or of causes yet to be identified. Despite the instances of lack of reproducibility that we review, and many others like them, the outlook is optimistic. First, because "lack of reproducibility is not necessarily bad news; it may herald new discoveries and signal scientific progress" (Nat. Phys. 16 (2020) 117-119). Second, and as the example about the measurement of the Newtonian constant of gravitation, G, illustrates, when faced with a reproducibility crisis the scientific community often engages in cooperative efforts to understand the root causes of the lack of reproducibility, leading to advances in scientific knowledge.
