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nteger partition and q-series sum-to-product identities, such as the Rogers-Ramanujan identities, lie at the intersection of combinatorics, number theory, and the representation theory of affine Lie algebras. This talk will focus on the method of atomic relations, which has been developed by Shashank Kanade and the author in recent years as a way to prove these identities. In some cases, computer output from this method can guide human-constructed proofs, while in other cases, our proofs are totally computer-generated. Applications of this method to problems involving cylindric partitions and colored partitions will also be discussed.