Space weather models endeavoring to connect remote observations to in-situ measurements at various locations in the heliosphere invariably require a coronal model to connect the photosphere magnetically to the inner heliosphere. The most famous and popular implementation of this connection is a potential field source surface (PFSS) model out to the source surface, typically located at 2.5 solar radii, combined with a Schatten current sheet (SCS) model. While the PFSS model is mostly understood, the SCS has been utilized in heliospheric physics for nearly 50 years with little understanding of it’s physical and mathematical underpinnings. In this overview article, I lay out the mathematical formalism of the SCS, describe how it differs from the PFSS, and summarize several techniques used to combine the PFSS and SCS to create a global coronal model from the photosphere to the inner heliosphere.