After a review of developments in the quantitative study of science, particularly since the early 1970s, I focus on two current main lines of ‘measuring science’ based on bibliometric analysis. With the developments in the Leiden group as an example of daily practice, the measurement of research performance and, particularly, the importance of indicator standardisation are discussed, including aspects such as interdisciplinary relations, collaboration, ‘knowledge users’. Several important problems are addressed: language bias; timeliness; comparability of different research systems; statistical issues; and the ‘theory-invariance’ of indicators. Next, an introduction to the mapping of scientific fields is presented. Here basic concepts and issues of practical application of these ‘science maps’ are addressed. This contribution is concluded with general observations on current and near-future developments, including network-based approaches, necessary ‘next steps’ are formulated, and an answer is given to the question ‘Can science be measured?’