One of the primary uses of graph theory in social network analysis, as applied to anthropology and the other social and behavioral sciences, is the identification of the "most important" actors in a social network. Such actors are usually termed "central" or "prestigious". Such identifications can be used by researchers to place the actors into distinct subgroups. In this paper, we present and discuss a variety of centrality and prestige measures, designed to highlight the difference between important and nonimportant actors. This paper reviews the existing literature on centrality and prestige, and at the same time, presents a synthesis of this methodology using an increasingly-known statistical model for social network data. Many of these methods might be new to social and behavioral scientists. Further, the review aspects of this paper are novel - no research has attempted to put centrality and prestige indices into a single framework. Further, the synthesis we present is new to the social network literature.