The field of cosmic microwave background (CMB) anisotropies has dramatically advanced over the last decade (cf. [White et al, 1994]), especially on its observational front. The observations have turned some of our boldest speculations about our Universe into a working cosmological model: namely, that the Universe is spatially flat, consists mainly of dark matter and dark energy, with the small amount of ordinary matter necessary to explain the light element abundances, and all the rich structure in it formed through gravitational instability from quantum mechanical fluctuations when the Universe was a fraction of a second old. Observations over the coming decade should pin down certain key cosmological parameters with unprecedented accuracy [Knox, 1995,Jungman et al, 1996,Bond et al, 1997,Zaldarriaga et al, 1997,Eisenstein et al, 1999]. These determinations will have profound implications for astrophysics, as well as other disciplines. Particle physicists, for example, will be able to study neutrino masses, theories of inflation impossible to test at accelerators, and the mysterious dark energy or cosmological constant.
For the twenty eight years between the discovery of the CMB [Penzias & Wilson, 1965] and the COBE DMR detection of 10-5 fluctuations in its temperature field across the sky [Smoot et al, 1992], observers searched for these anisotropies but found none except the dipole induced by our own motion [Smoot et al, 1977]. They learned the hard way that the CMB is remarkably uniform. This is in stark contrast to the matter in the Universe, organized in very non-linear structures like galaxies and clusters. The disparity between the smooth photon distribution and the clumpy matter distribution is due to radiation pressure. Matter inhomogeneities grow due to gravitational instability, but pressure prevents the same process from occuring in the photons. Thus, even though both inhomogeneities in the matter in the Universe and anisotropies in the CMB apparently originated from the same source, these appear very different today.
Since the photon distribution is very uniform, perturbations are small, and linear response theory applies. This is perhaps the most important fact about CMB anisotropies. Since they are linear, predictions can be made as precisely as their sources are specified. If the sources of the anisotropies are also linear fluctuations, anisotropy formation falls in the domain of linear perturbation theory. There are then essentially no phenomenological parameters that need to be introduced to account for non-linearities or gas dynamics or any other of a host of astrophysical processes that typically afflict cosmological observations.
CMB anisotropies in the working cosmological model, which we briefly review in §2, fall almost entirely under linear perturbation theory. The most important observables of the CMB are the power spectra of the temperature and polarization maps. Theory predicts, and now observations confirm, that the temperature power spectrum has a series of peaks and troughs. In §3, we discuss the origin of these acoustic peaks and their cosmological uses. Although they are the most prominent features in the spectrum, and are the focus of the current generation of experiments, future observations will turn to even finer details, potentially revealing the physics at the two opposite ends of time. Some of these are discussed in §4. Finally, the past few years have witnessed important new advances, introduced in §5, from a growing body of CMB data analysts on how best to extract the information contained in CMB data. Some of the fruits of this labor have already spread to other fields of astronomy.