Quantitative literacy---the use of mathematics to describe and understand the world---is an essential skill. One facet of quantitative literacy in physics is covariational reasoning: how changes in one quantity affect changes in another, related quantity. Research 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 has shown that quantitative literacy is unlikely to improve in physics classrooms without direct instruction. 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. We characterize and operationalize physics covariational reasoning through a series of studies that examine how physics experts reasoned while generating graphical models. Our results, 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 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 present two assessment tools, the Physics Inventory of Quantitative Literacy (PIQL) and the Generalized Equation-based Reasoning inventory of Quantity and Negativity (GERQN), designed to measure physics quantitative literacy across a range of student populations. We conclude with how these pieces can be used to guide development of instructional materials to improve students' physics quantitative literacy.