Secure device pairing (SDP) schemes have been developed to facilitate secure communications among smart devices, both personal mobile devices and Internet of Things devices. Comparison and assessment of SDP schemes is troublesome, because each scheme makes different assumptions about out-of-band channels and adversary models, and are driven by their particular use-cases. A conceptual model that facilitates meaningful comparison among SDP schemes is missing. We provide such a model. In this paper, we survey and analyze a wide range of SDP schemes that are described in the literature, including a number that have been adopted as standards. A system model and consistent terminology for SDP schemes are built on the foundation of this survey, which are then used to classify existing SDP schemes into a taxonomy that, for the first time, enables their meaningful comparison and analysis. The existing SDP schemes are analyzed using this model, revealing common systemic security weaknesses among the surveyed SDP schemes that should become priority areas for future SDP research, such as improving the integration of privacy requirements into the design of SDP schemes. Our results allow SDP scheme designers to create schemes that are more easily comparable with one another, and to assist the prevention of persisting the weaknesses common to the current generation of SDP schemes.