We show that, leaving aside accelerated cosmic expansion, all experimental data in high energy physics that are commonly agreed to require physics beyond the Standard Model can be explained when completing the model by three right-handed neutrinos that can be searched for using present-day experimental techniques. The model that realizes this scenario is known as the Neutrino Minimal Standard Model (νMSM). In this article we give a comprehensive summary of all known constraints in the νMSM, along with a pedagogical introduction to the model. We present the first complete quantitative study of the parameter space of the model where no physics beyond the νMSM is needed to simultaneously explain neutrino oscillations, dark matter, and the baryon asymmetry of the Universe. The key new point of our analysis is leptogenesis after sphaleron freeze-out, which leads to resonant dark matter production, thus evading the constraints on sterile neutrino dark matter from structure formation and x-ray searches. This requires one to track the time evolution of left- and right-handed neutrino abundances from hot big bang initial conditions down to temperatures below the QCD scale. We find that the interplay of resonant amplifications, CP-violating flavor oscillations, scatterings, and decays leads to a number of previously unknown constraints on the sterile neutrino properties. We furthermore reanalyze bounds from past collider experiments and big bang nucleosynthesis in the face of recent evidence for a nonzero neutrino mixing angle θ13. We combine all our results with existing constraints on dark matter properties from astrophysics and cosmology. Our results provide a guideline for future experimental searches for sterile neutrinos. A summary of the constraints on sterile neutrino masses and mixings has appeared in Canetti et al. [ Phys. Rev. Lett. 110 061801 (2013)]. In this article we provide all details of our calculations and give constraints on other model parameters.