Within supersymmetric grand unified theories, cosmic strings are generically formed at the end of a hybrid inflationary era. However, cosmic microwave background measurements imply severe constraints on the allowed cosmic strings contribution to the temperature anisotropies. In the framework of supersymmetry, I will study F- and D-term inflation and I will set constraints on the free parameters (mass scales and couplings) of the models, so that there is compatibility between mixed models (inflation + cosmic strings) and current measurements. Recently there is a revival in interest for cosmic strings, since ina ddition, superstrings could play the role of cosmic strings in theories with large extra dimensions and moreover it may be that cosmic strings have been already seen in the sky.