Abstract Eliciting the preferences of a set of agents over a set of alternatives is a problem of fundamental importance in social choice theory. Prior work on this problem has studied the query complexity of preference elicitation for the unrestricted domain and for the domain of single peaked preferences. In this paper, we consider the domain of single crossing preference profiles and study the query complexity of preference elicitation under various settings. We consider two distinct situations: when an ordering of the voters with respect to which the profile is single crossing is known versus when it is unknown. We also consider random and sequential access models. The main contribution of our work is to provide polynomial time algorithms with low query complexity for preference elicitation in all the above cases. Further, we show that the query complexities of our algorithms are optimal up to constant factors for all but one of the above cases.