First gradient continuum models, while being particularly suitable for natural materials, have poor prediction power when architectured materials are concerned. Nowadays the challenge is indeed to prescribe the micro-scale mechanical characteristics needed to get a specific desired behavior at the macro-scale. In particular, continua with inextensible fibers are today employed in very wide class of applications, from the design of special fabrics to tissue engineering. The scientific problems posed by these applications involve many areas, as the theoretical coverage, the designing of suitable experimental procedures and the development of specific numerical tools are all crucial aspects of the general picture.