Recent years have seen the development of effective methods and computer programs to automatically detect sentiment in text. These programs have been used primarily to analyse online texts, both for research and commercial applications, and are valuable to help gain insights into public opinions about the topics, products and issues discussed online. Automated sentiment analysis has big data applications because it allows huge amounts of text to be processed rapidly, enabling sentiment-related insights to be gained that might not otherwise be detectable from small amounts of data. This chapter reviews the main different sentiment analysis methods, including both lexical and machine learning approaches, as well as the main tasks, such as polarity detection, sentiment strength detection, and fine-grained emotion detection. It also covers important related tasks, such as the need to customise software designed for one type of text before it can be applied efficiently to another and to detect the target of any sentiment expression. The chapter also reviews sentiment analyses research applications involving either big data or small scale samples of online texts, showing the range of current applications as well as the potential to deploy the methods to investigate a wide range of issues. Most of this research focuses on the social sciences, and on issues for which public opinion data is relevant. Some of the research also analyses the affective component of online communication within the social web in contexts such as political debates and communication between friends, when sentiment forms an important component of the interactions.