Astronomical data are often provided with information about the “real-world” coordinates that correspond to pixel coordinates. This mapping is the essence of the “World Coordinate System (WCS)” concept. In addition to FITS WCS (the origin of the “WCS” term), other WCS standards/representations are becoming necessary for new missions and observatories (e.g., the James Webb Space Telescope or the Large Synoptic Survey Telescope). In order to build functionality in Astropy and affiliated packages that may require use of WCS, having to deal with different kinds of WCS objects with different APIs will be essentially impossible. Thus, the purpose of this APE is to define a standardized interface to WCS objects based on simple objects (strings, scalars, and arrays). Packages implementing WCS objects will then be able to either modify their classes to conform to the API recommended here or build thin wrappers that conform to the API. The APE also provides a recommendation for a high-level object to be implemented in Astropy that understands familiar Python objects such as SkyCoord, Time, and other Astropy classes. Note: this APE14 was originally accepted on 2018-Feb-28, but due to issues with implementation was significantly revised on 2018-November-9. This Zenodo record is for the revised version.