In this chapter, I provide a discussion of selected discoveries that have been made about students' conceptions of probability. I also include a discussion of some trends in student performace on probability items on the 1996 National Assessment of Educational Progress (NAEP). In light of what is known about student thinking and performance in probability, I present some suggestions for the teaching of probability, I point out that a separation of research discussions of probability and statistics is artificial, just as artificial as the separation of data and chance when teaching. Principles and Standards for School Mathematics (NCTM, 2000) aptly places probability and statistics under one shared heading. I believe the most interesting research questions for the future reside in the joint realm of the areas of probability and statistics, just as the most interesting teaching challenges for the future lie in making interconnections between these two areas.