In some types of cosmological models, it is postulated that when the universe expanded and cooled, the underlying 'scalar' field which produced inflation when the universe was 10^-34 seconds old, crystallized into numerous topological defects. The simplest is the monopole defect, the next most complicated is the cosmic string. These strings are 1-dimensional lines of warped space-time along which the density is 'singular' or nearly so. They weigh 10^-5 grams for each segment that is 10^-33 centimeters long or so. They may be millions of light years long and thread through our space like spaghetti in a colander. Gravitational lens searches suggest that, if they exist at all, they are probably very rare because they should produce multiple images of background galaxies and quasars, and the ones we find are accounted for by the known distribution of galaxies.