Twitter has arguably been the most popular among the data sources that form the basis of so-called altmetrics. Tweets to scholarly documents have been heralded as both early indicators of citations as well as measures of societal impact. This chapter provides an overview of Twitter activity as the basis for scholarly metrics from a critical point of view and equally describes the potential and limitations of scholarly Twitter metrics. By reviewing the literature on Twitter in scholarly communication and analyzing 24 million tweets linking to scholarly documents, it aims to provide a basic understanding of what tweets can and cannot measure in the context of research evaluation. Going beyond the limited explanatory power of low correlations between tweets and citations, this chapter considers what types of scholarly documents are popular on Twitter, and how, when and by whom they are diffused in order to understand what tweets to scholarly documents measure. Although this chapter is not able to solve the problems associated with the creation of meaningful metrics from social media, it highlights particular issues and aims to provide the basis for advanced scholarly Twitter metrics.