A central pillar of modern cosmology is the near-isotropy of the CMB, compatible with a perturbed FLRW model of the universe. The small deviations from isotropy in the CMB temperature contain a wealth of information. Temperature anisotropies due to inhomogeneities were predicted by Sachs and Wolfe (1967) soon after the discovery of the CMB in 1965 by Penzias and Wilson. Shortly afterwards, polarization was predicted in models with anisotropy in the expansion rate around the time of recombination (Rees, 1968). The detailed physics of CMB fluctuations in almost-FLRW models was essentially understood for models with only baryonic matter by 1970 (Silk, 1968, Peebles, 1968, Zel'dovich, Kurt and Sunyaev, 1968, Peebles and Yu, 1970, Sunyaev and Zel'dovich, 1970). By the early 1980s, CDM was included (Peebles, 1982, Bond and Efstathiou, 1984). Further milestones included the effect of spatial curvature (Wilson, 1983), polarization (Kaiser, 1983, Bond and Efstathiou, 1984) and gravitational waves (Dautcourt, 1969, Polnarev, 1985). All of this work used the standard metric-based approach to cosmological perturbation theory, but CMB physics has also been studied extensively in the 1+3-covariant approach (Ellis, Matravers and Treciokas, 1983b, Ellis, Treciokas and Matravers, 1983, Stoeger, Maartens and Ellis, 1995, Maartens, Ellis and Stoeger, 1995a,b, Dunsby, 1997, Uzan, 1998, Challinor and Lasenby, 1998, 1999, Maartens, Gebbie and Ellis, 1999, Challinor, 2000a,b, Lewis, Challinor and Lasenby, 2000, Gebbie and Ellis, 2000, Gebbie, Dunsby and Ellis, 2000, Lewis, 2004a,b, Pitrou, 2009).