The cosmic microwave background (CMB) represents a unique source for the
study of gravitational lensing. It is extended across the entire sky, partially
polarized, located at the extreme distance of z=1100, and is thought to have
the simple, underlying statistics of a Gaussian random field. Here we review
the weak lensing of the CMB, highlighting the aspects which differentiate it
from the weak lensing of other sources, such as galaxies. We discuss the
statistics of the lensing deflection field which remaps the CMB, and the
corresponding effect on the power spectra. We then focus on methods for
reconstructing the lensing deflections, describing efficient quadratic
maximum-likelihood estimators and delensing. We end by reviewing recent
detections and observational prospects.Comment: 21 pages, 5 figures. Invited review for GRG special issue on
gravitational lensin
