  Hybrid inflation within supersymmetric grand unified theories, as well as
inflation through brane collisions within braneworld cosmological models, lead
to the formation of one-dimensional defects. Observational data, mainly from
the cosmic microwave background temperature anisotropies but also from the
gravitational wave background, impose constraints on the free parameters of the
models. I review these inflationary models and discuss the constraints from the
currently available data.
