Once the acoustic peaks in the temperature and polarization power spectra have been scaled, the days of splendid isolation of cosmic microwave background theory, analysis and experiment will have ended. Beyond and beneath the peaks lies a wealth of information about the evolution of structure in the Universe and its origin in the early universe. As CMB photons traverse the large scale structure of the Universe on their journey from the recombination epoch, they pick up secondary temperature and polarization anisotropies. These depend on the intervening dark matter, dark energy, baryonic gas density and temperature distributions, and even the existence of primordial gravity waves, so the potential payoff of their detection is enormous. The price for this extended reach is the loss of the ability both to make precise predictions, due to uncertain and/or non-linear physics, and to make precise measurements, due to the cosmic variance of the primary anisotropies and the relatively greater importance of galactic and extragalactic foregrounds.
We begin in §4.1 with a discussion of the matter power spectrum to set the framework for the discussion of secondary anisotropies. Secondaries can be divided into two classes: those due to gravitational effects and those induced by scattering off of electrons. The former are treated in §4.2 and the latter in §4.3. Secondary anisotropies are often non-Gaussian, so they show up not only in the power spectra of §2, but in higher point functions as well. We briefly discuss non-Gaussian statistics in §4.4. All of these topics are subjects of current research to which this review can only serve as introduction.