The paper reviews today’s most successful approaches to sentiment analysis of massive datasets of user-generated texts, including those from Twitter. We define today’s most developed areas of sentiment studies and their limitations, as well as methodological, technological, and other challenges that sentiment analysis faces in its variations across the world. We also group the existing research into clusters based on several criteria, including presence/absence of machine learning, unit of analysis, and object of study. We show that the creation of cross-cultural multilingual sentiment analysis and tools for it is a major task that today’s sentiment studies face; such tools would allow detecting sentiment across a range of languages and cultures. We assess the existing tools for multi-lingual sentiment analysis and suggest a conceptual framework for future studies of sentiment in different language domains of Twitter.