Quantitative literacy---the use of mathematics to describe and understand the world---is an essential skill. Physics has an opportunity to contribute to how students develop quantitative literacy, as much of physics curriculum centers on making sense of quantitative models. One facet of quantitative literacy in physics is covariational reasoning: how changes in one quantity affect changes in another, related quantity. Covariational reasoning is at the heart of developing and making sense of quantitative models, and is central to graphical reasoning. Much of the research on covariation lies in mathematics education; the language of covariation has only recently begun to be used amongst physics education research. Research in physics and mathematics education has demonstrated that reasoning mathematically in physics contexts is distinct from reasoning mathematically in a context-free way. Early indications suggest that, similarly, covariational reasoning is likely different in physics contexts than in mathematics. Moreover, research into quantitative literacy more generally has shown that it is unlikely to improve in physics classrooms without direct instruction. Therefore, there is a need to characterize and understand physics covariational reasoning towards developing instructional activities that can be used in physics classrooms to help students develop quantitative literacy. The research presented in this dissertation represents a collection of work that provides a foundation for instructional activity development. We describe research into characterizing and operationalizing physics covariational reasoning through a series of studies that examine how physics experts reasoned while generating graphical models. The results of this study, together with prior research in the field, are organized into a framework of covariational reasoning: the Covariational Reasoning in Physics (CoRP) framework. We present this framework in this dissertation, and describe how it can be used towards identifying learning outcomes for introductory physics courses and beyond, identifying proto-expert resources that students may already have when entering physics courses, and developing instructional interventions that attend to improving students' quantitative literacy. We then present two short reflections on two assessment tools, the Physics Inventory of Quantitative Literacy (PIQL) and the Generalized Equation-based Reasoning inventory of Quantity and Negativity (GERQN), that are designed to measure physics quantitative literacy across a wide range of student populations. These assessment tools can be used to measure the impact of instruction on students' physics quantitative literacy, and thus are a necessary tool towards designing activities that are supported by research. This dissertation concludes with a reflection on how these pieces can be used together for future steps towards the development of instructional materials. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]