Ever since the links between the development of new technologies and economic growth became evident, researchers have attempted to study how the creation of knowledge fosters progress. If pushing the frontier of knowledge has an impact on progress and well-being, it is essential to pursue some form of science policy. Policymakers rely on the scholarly work of researchers in order to understand the likely impact of new policies and investments, and evaluate the state of the art in science and innovation policy. Therefore, the work of social scientists, economists of science and information scientists, among others, is vital to the characterisation, understanding and management of science. In recent years, the availability and quality of science data (including bibliographic data and metadata, funding, relational databases, ontologies and classifications) has boosted the empirical work in the depiction of the organisational structure of science. In turn, policy analysis has been able to accurately identify many unsuspected effects of past investments and policy decisions both at the macro and micro level. Using topic models, we develop a novel method for evaluating the robustness of different text-to-text similarity models. Employing that procedure, we find that the neural-network-based paragraph embeddings approach seems capable of providing statistically robust estimates of document--document similarities. Finding methods to estimate the similarity between individual publications is an area of long-standing interest in the information science and scientometrics communities. These techniques enable researchers to build indicators and classification methods based on the analysis of large text corpora. We show that the most widely used techniques suffer from inconsistencies upon retraining, and provide a procedure to evaluate and compare the quality of different methods, regardless of the data. Next, we present a game-theoretic model of rewards to scientific contributions. Our model of science may help explain the resulting social organisation of science from a simple social dilemma model. We model a researcher's payoff as a common-pool resource game, intrinsically connecting the appropriability of scientific output to a scientist's optimal strategy. This simple model of reward allocation sheds new light on a variety of behaviours that have been observed amongst researchers. Finally, we propose an empirical analysis of the relationship between basic knowledge generation and spillovers to innovation. Using the United States' 2001 ban on federal funding of human embryonic stem cells (hESC), we disentangle the effect that policy had on downstream innovation. We employ recently developed data on patent-to-scientific-article citations to measure the spillovers, and we characterise the causal impact of the policy on subsequent innovation with a difference-in-differences estimator. Our estimates suggest that in the years following the policy, scholarly publications subject to the ban received 65 to 80 per-cent fewer patent citations than the control group. We then apply topic modelling techniques to examine changes in the direction of science. In particular we build a topic-variety metric. Our findings show that variety decreased in the aftermath of the policy. Our results suggest that even the most modest policy changes have a profound impact on downstream innovation and the advancement at the frontier.