In this study, we explore the citedness of research data, its distribution over time and its relation to the availability of a digital object identifier (DOI) in the Thomson Reuters database Data Citation Index (DCI). We investigate if cited research data “impacts” the (social) web, reflected by altmetrics scores, and if there is any relationship between the number of citations and the sum of altmetrics scores from various social media platforms. Three tools are used to collect altmetrics scores, namely PlumX, ImpactStory, and Altmetric.com, and the corresponding results are compared. We found that out of the three altmetrics tools, PlumX has the best coverage. Our experiments revealed that research data remain mostly uncited (about 85 %), although there has been an increase in citing data sets published since 2008. The percentage of the number of cited research data with a DOI in DCI has decreased in the last years. Only nine repositories are responsible for research data with DOIs and two or more citations. The number of cited research data with altmetrics “foot-prints” is even lower (4–9 %) but shows a higher coverage of research data from the last decade. In our study, we also found no correlation between the number of citations and the total number of altmetrics scores. Yet, certain data types (i.e. survey, aggregate data, and sequence data) are more often cited and also receive higher altmetrics scores. Additionally, we performed citation and altmetric analyses of all research data published between 2011 and 2013 in four different disciplines covered by the DCI. In general, these results correspond very well with the ones obtained for research data cited at least twice and also show low numbers in citations and in altmetrics. Finally, we observed that there are disciplinary differences in the availability and extent of altmetrics scores.