Affective computing is the study and development of devices that can recognize emotions through various modes such as video, audio and text automatically. In this thesis, I focus on the problem of affective computing in short texts, in particular, tweets. Withtheevolutionofsocialmediaintherecentyears,therehasbeena rapid growth of interactions that take occur online, which are expressive in terms of emotion.Internet users today have several diverse methods of being expressive through text, such as by using abbreviations, emoticons and hashtags. I use traditional lexical features and word embeddings to extract semantic and lexical information from the input text. I develop models ranging from linear and tree-based models to deep neural networks to perform emotion detection on Tweets. I create an ensemble of these methods to make my final predictions. I evaluate the ensemble on the SemEval 2018 dataset containing intensity and class annotations for emotions in tweets. I finally perform an error analysis of these algorithms and highlight potential areas of improvement.