Emotions are a central aspect of communication. Consequently, emotion analysis (EA) is a rapidly growing field in natural language processing (NLP). However, there is no consensus on scope, direction, or methods. In this paper, we conduct a thorough review of 154 relevant NLP publications from the last decade. Based on this review, we address four different questions: (1) How are EA tasks defined in NLP? (2) What are the most prominent emotion frameworks and which emotions are modeled? (3) Is the subjectivity of emotions considered in terms of demographics and cultural factors? and (4) What are the primary NLP applications for EA? We take stock of trends in EA and tasks, emotion frameworks used, existing datasets, methods, and applications. We then discuss four lacunae: (1) the absence of demographic and cultural aspects does not account for the variation in how emotions are perceived, but instead assumes they are universally experienced in the same manner; (2) the poor fit of emotion categories from the two main emotion theories to the task; (3) the lack of standardized EA terminology hinders gap identification, comparison, and future goals; and (4) the absence of interdisciplinary research isolates EA from insights in other fields. Our work will enable more focused research into EA and a more holistic approach to modeling emotions in NLP.