Customers are human beings who express their emotions openly on social media platforms. There is a wealth of social media data that companies can make use of to improve their business decision making and tailor their marketing strategies. In order to benefit from this, organizations need to apply computational methods, which can save time and effort rather than applying traditional consumer research approaches, such as surveys or interviews. The purpose of this study is to investigate existing computational studies on detecting consumer emotions from social media data. We conducted a systematic literature review on articles published in ScienceDirect, IEEE Explore, ACM Digital Library, and Emerald Insight from the period 2009-2017. The aim was to discover how social media data was extracted, how large datasets were used in detecting emotions, the type of computational methods used, and the accuracy of the results obtained from the existing studies. Most of the studies were focused on sentiment analysis and different machine learning algorithms. The computational methods were applied in business decision making and marketing functions. Practical scenarios included emotion detection in customer reviews and sentiment analysis of retail brands. Based on these studies, we have uncovered situations where the results of the analysis are either sufficiently accurate or supportive for decision making. We provide recommendations for organizations and managers on developing their resources to make use of different computational methods for emotion and sentiment detection. Finally, we present the limitations of these methods and provide recommendations for aligning future research studies toward big social data analytics on customer emotions.