Frontiers in Complex Dynamics

this article we survey a small constellation of such conjectures, centering around the density of hyperbolic rational maps --- those which are dynamically the best behaved. We discuss some of the evidence and logic underlying these conjectures, and sketch recent progress towards their resolution. Our presentation entails only a brief account of the basics of complex dynamics; a more systematic exposition can be found in the survey articles [Dou1], [Bl], and [EL], the recent books [Bea] and [CG], and Milnor's lecture notes [Mil4]