The cosmic microwave background: a theorist’s perspective

We review the role of the temperature anisotropies and polarization of the cosmic microwave background (CMB) radiation in constraining the cosmological model. We put particular emphasis on the major milestones that have been passed, and CMB constraints on early-universe physics. We also look ahead, surveying what we hope to learn from the next generation of instruments targeting the small-scale imprint of reionization and gravitational lensing, and the large-scale polarization signature of gravitational waves.