In recent joint work with Jim Haglund and Jeff Remmel, we conjecture a combinatoral interpretation for a certain symmetric function appearing in the study of Macdonald polynomials and diagonal harmonics. This conjecture, which we call the Delta Conjecture, generalizes the famous Shuffle Conjecture, formulated by Haglund, Haiman, Remmel, Loehr and Ulyanov and recently proved by Carlsson and Mellit. I will explain our conjecture and discuss some of the cases we can prove at this point. These cases are appealing not just because they are tractable, but because they inspire new ways to think about classical combinatorial objects such as ordered set partitions, upper triangular matrices, and parking functions.