Can alternative metrics (altmetrics) data be used to measure societal impact? We wrote this literature overview of empirical studies in order to find an answer to this question. The overview includes two parts. The first part, “societal impact measurements”, explains possible methods and problems in measuring the societal impact of research, case studies for societal impact measurement, societal impact considerations at funding organizations, and the societal problems that should be solved by science. The second part of the review, “altmetrics”, addresses a major question in research evaluation, which is whether altmetrics are proper indicators for measuring the societal impact of research. In the second part we explain the data sources used for altmetrics studies and the importance of field-normalized indicators for impact measurements. This review indicates that it should be relevant for impact measurements to be oriented towards pressing societal problems. Case studies in which societal impact of certain pieces of research is explained seem to provide a legitimate method for measuring societal impact. In the use of altmetrics, field-specific differences should be considered by applying field normalization (in cross-field comparisons). Altmetrics data such as social media counts might mainly reflect the public interest and discussion of scholarly works rather than their societal impact. Altmetrics (Twitter data) might be especially fruitfully employed for research evaluation purposes, if they are used in the context of network approaches. Conclusions based on altmetrics data in research evaluation should be drawn with caution.