Wireless communications technologies play an irreplaceable role in emergency and disaster relief situations. It is generally acknowledged that the existing public safety (PS) wireless communications facilities frequently fall short of meeting users' needs in many critical situations. Emergency scenarios usually lead to exceptionally high traffic loads, and the lack of network capacity is one of the major limitations to overcome. In this context, this article first discusses about several dimensions that enable increased capacity in emergency scenarios, and then the attention is placed on the role of spectrum sharing as one of these key dimensions. In this regard, a comprehensive view of possible spectrum-sharing models for emergency communications is developed. The key principles underlying each sharing model are given, and its applicability is described through illustrative examples, where it is made evident that cognitive radio (CR) technology constitutes a major technological enabler for their realization. Finally, a discussion on the feasibility of each of the spectrum sharing models is addressed.