Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions “What is observable?”, “What in the Universe is knowable?” and “What are the fundamental limits to cosmological knowledge?”. We then describe the methodology for investigation: theoretical hypotheses are used to model, predict and anticipate results; data is used to infer theory. We illustrate with concrete examples of principled analysis approaches from the study of cosmic microwave background anisotropies and surveys of large-scale structure, culminating in a summary of the highest-precision probe to date of the physical origin of cosmic structures: the Planck 2013 constraints on primordial non-Gaussianity.