As a rapidly developing research area, the science of science (SciSci) is devoted to quantifying, understanding, and predicting scientific research and its outputs. While much progress has been achieved on impact measuring and the collaboration network, the research on the dynamical evolution of whole research systems is much less studied. This is the key question we try to answer in this dissertation: how do we quantify, understand, and predict the evolution of scientific research, and more generally, the processes of innovation? Not only can the answer to this question help universities and research institutes recruit new scientists, and point governments and companies to the most fruitful research frontier to fund, it also opens up many new science questions: for example, are there any laws governing the enterprise of scientific research? To answer this question, we first built a data-driven framework for studying knowledge evolution. Using the American Physical Society (APS) publications data sets, we constructed year-to-year bibliographic coupling networks, and identified validated communities-topical clusters (TCs)-that represent different research fields in them. We then visualized their evolutionary relationships in the form of alluvial diagrams, and showed how they remain intact through APS journal splits. Quantitatively, we saw that most fields 11 12 Abstract undergo weak mixing, and it is rare for a field to remain isolated or undergo strong mixing. The sizes of fields obey a simple linear growth with recombination. We can also reliably predict the merging between two fields, but not for the considerably more complex splitting. We reported a case study of two fields that underwent repeated merging and splitting around 1995, and how these Kuhnian events are correlated with breakthroughs on Bose-Einstein condensation (BEC), quantum teleportation, and slow light. This impact showed up quantitatively in the citations of the BEC field as a larger proportion of references from during and shortly after these events. In addition to this empirical study of the APS data set, we also used the linguistic information available in their abstracts to study how scientific memes evolve during knowledge evolution. This can help us gain a more complete understanding of knowledge evolution beyond citations. We found that particular memes are associated with particular TCs, making memes good labels for the TCs' research contents, at the same time making the alluvial diagram more comprehensible. Like a TC, a meme also has a complex evolution process. We measured the co-occurrence probability for meme pairs, and found 'quantum' and 'optical' grew closer since 1981, which is consistent with the rise of quantum optics. The co-evolution between memes and TCs is also discussed. Given the close relationship between evolution processes and scientific breakthroughs, it is important to be able to predict the future events. Having the predictive features describing a given TC and its known evolution in the next year, we can train a m...