We present a method for identifying groups of test examples—slices—on which a pre-trained model under-performs, a task now known as slice discovery. We formalize coherence, a requirement that erroneous predictions within returned slices should be wrong for the same reason, as a key property that a slice discovery method should satisfy. We then leverage influence functions (Koh & Liang, 2017) to derive a new slice discovery method, InfEmbed, which satisfies coherence by returning slices whose examples are influenced similarly by the training data. InfEmbed is computationally simple, consisting of applying K-Means clustering to a novel representation we deem influence embeddings. Empirically, we show InfEmbed outperforms current state-of-the-art methods on 2 benchmarks, and is effective for model debugging across several case studies.