The relationship between context incongruity and sarcasm has been studied in linguistics. We present a computational approach to harness context incongruity as a basis for sarcasm detection. Our statistical sarcasm classifiers incorporate two kinds of incongruity features: explicit and implicit. We show the benefit of our incongruity features for two text forms - tweets and discussion forum posts. Our approach also outperforms two past works (with F-score improvement of 10-20\%). We also show how our features can capture inter-sentential incongruity.