We present a method for identifying groups of test examples---slices---on which a model under-performs, a task now known as slice discovery. We formalize coherence---a requirement that erroneous predictions, within a slice, should be wrong for the same reason---as a key property that any slice discovery method should satisfy. We then use influence functions 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 simple, and consists of applying K-Means clustering to a novel representation we deem influence embeddings. We show InfEmbed outperforms current state-of-the-art methods on 2 benchmarks, and is effective for model debugging across several case studies.