A key principle of brain organization is the functional integration of brain regions into interconnected networks. Functional MRI scans acquired at rest offer insights into functional integration via patterns of coherent fluctuations in spontaneous activity, known as functional connectivity. These patterns have been studied intensively and have been linked to cognition and disease. However, the field is fractionated. Diverging analysis approaches have segregated the community into research silos, limiting the replication and clinical translation of findings. A primary source of this fractionation is the diversity of approaches used to reduce complex brain data into a lower-dimensional set of features for analysis and interpretation, which we refer to as brain representations. In this Primer, we provide an overview of different brain representations, lay out the challenges that have led to the fractionation of the field and that continue to form obstacles for convergence, and propose concrete guidelines to unite the field.