  We provide a pedagogical overview of defect models of structure formation. We
first introduce the concept of topological defect, and describe how to classify
them. We then show how defects might be produced in phase transitions in the
Early Universe and approach non-pathological scaling solutions. A very
heuristic account of structure formation with defects is then provided,
following which we introduce the tool box required for high precision
calculations of CMB and LSS power spectra in these theories. The decomposition
into scalar vector and tensor modes is reviewed, and then we introduce the
concept of unequal-time correlator. We use isotropy and causality to constrain
the form of these correlators. We finally show how these correlators may be
decomposed into eigenmodes, thereby reducing a defect problem to a series of
``inflation'' problems. We conclude with a short description of results in
these theories and how they fare against observations. We finally describe yet
another application of topological defects in cosmology: baryogenesis.
