Observations of the cosmic microwave background (CMB) have played a critical role in establishing the current cosmological concordance model. Next generation CMB experiments promise to go even further, and image the very birth of the universe by observing primordial gravitational waves created during the Big Bang. However, observing this signal will be a tremendous challenge, as the expected signal can easy be contaminated by systematic uncertainties both from confusing radiation from the Milky Way and from instrumental imperfections. In this talk, I will describe the BeyondPlanck project, which developed the world's first end-to-end Bayesian CMB analysis code, accounting for both instrumental and astrophysical uncertainties, and applied this to the Planck LFI data set. I will argue that this approach not only sets a new standard for CMB analysis, but also that the main ideas are applicable to any experiment for which systematic error propagation is the main limiting factor.