In 1956, Alder conjectured that the number of d-distinct partitions of an integer n is always greater than or equal to the number of partitions of n into parts congruent to 1 or -1 modulo d+3. This conjecture generalized well known identities of Euler, Rogers and Ramanujan, and Schur. However, it was not until 2010 that Alder’s Conjecture was proven to be true. In this talk, we overview the history and partial results from over those 60+ years. We also discuss a recent analogue of the Alder Conjecture which generalizes the second Rogers-Ramanujan identity. Finally, we discuss ongoing work with Holly Swisher to compute upper bounds on d-distinct partitions.