In this review we describe the formation and evolution of topological defects which may form during symmetry breaking phase transitions in the early Universe. After an introduction to cosmological perturbation theory, we discuss the scale invariant spectrum of fluctuations induced by defects in a homogeneous and isotropic universe. We describe the numerical calculation of anisotropies and polarization of the cosmic microwave background and show that the pattern of acoustic peaks, characteristic of inflationary models and observed in the data, is absent for global O( N) defects and for cosmic strings. We reveal the origin of this result and we study whether more general ‘scaling causal seeds’ may be brought in agreement with present data. We also investigate mixed models where cosmological perturbations come from the amplification quantum fluctuations generated during an inflationary phase and from defects created at the end of inflation.