The relationship between context incongruity and sarcasm has been studied in linguistics. We present a computational system that harnesses 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 system also outperforms two past works (with Fscore improvement of 10-20%). We also show how our features can capture intersentential incongruity.