Physics education research has benefited from initial early successes based on uncovering common student misconceptions for a variety of topics.  Based on an understanding of common student difficulties, curriculum developers have been able to create instructional materials that took advantage of active learning strategies to effectively address these misconceptions for many students.  In this talk, I will first give some examples of research of this type.  Implicit in this research is the belief that students have strongly-held ideas about the physics topic under investigation, and that questions asked by instructors and physics education researchers are eliciting these ideas.  In the past decade, this belief has been challenged by a growing segment of the research community, and some researchers are using different models for what happens when we ask questions of our students.  I will describe these alternate models and an experiment intended to test the viability of one model for student thinking.  Finally, I will give an introductory description of the study of student epistemologies, which is emerging as an important factor influencing student learning in physics.