Since Bennequin's work, it has been well-known that in 3-dimensional topology, there is a dichotomy between tight and overtwisted contact structures. Overtwisted contact structures are well-understood through their classification due to Y. Eliashberg but the study of tight contact structures from a 3-dimensional perspective is still at its early stage. In most studies, contact structures are always considered oriented. (Recall that a contact 3-manifold is always orientable but its contact structure does not have to be). It is often thought that if one has to deal with nonorientable contact structures, one may work with its orientation double cover. Although it is true that the tightness of the double cover implies the tightness of the corresponding nonorientable contact structure, our motivation is to realize that one cannot merely switch to the orientation double cover without loss of information when studying tightness. In this talk, we will systematically study the tightness of nonorientable contact structures and produce examples of 3-manifolds equipped with nonorientable tight contact structures for which the orientation double cover is overtwisted.