Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we expand on the current knowledge base on graphical forms to contribute an empirically based catalog. We also situate our cognitively oriented work in relation to research that has emphasized (a) misconceptions and (b) social practices. In addition, we draw connections to the research on covariational reasoning. We end with implications regarding how graphical forms contribute to our understanding of students' graphical reasoning and how instructors can support students.