In cosmology, as in other areas of astrophysics, we are constrained to make observations of unrepeatable events (such as the Big Bang), and so have to proceed by statistical inference. The Bayesian approach involves treating models and parameters similarly to data, as unknown variables with their own underlying probability distributions. However, as data from cosmological observables increases in constraining power, the opportunity arises for tensions between the different data sets, where the statistical limits on derived on certain parameters appears not to be coincident. This tensions can be generated either by an insufficient model, and so indicates the presence of new physics, by undiagnosed systematic errors, or simply by random statistical chance. In my talk I discuss different methods for diagnosing tensions, and show how these have been applied to the observed parameter tension between the cosmic microwave background data and measurements of the weak lensing shear power spectrum.