In an information system a key role is played by the underlying data schema. This article starts out from the view that the entire modelling process of an information system's data schema can be seen as a schema transformation process. A transformation process that starts out with an initial draft conceptual schema and ends with an internal database schema for some implementation platform. This allows us to describe the transformation process of a database design as an evolution of a schema through a universe of data schemas. Doing so allows a better understanding of the actual design process, countering the problem of ‘software development under the lamppost’. Even when the information system design is finalised, the data schema can evolve further due to changes in the requirements on the system. We present a universe of data schemas that allows us to describe the underlying data schemas at all stages of their development. This universe of data schemas is used as a case study on how to describe the complete evolution of a data schema with all its relevant aspects. The theory is general enough to cater for more modelling concepts, or different modelling approaches. To actually model the evolution of a data schema we present a versioning mechanism that allows us to model the evolutions of the elements of data schemas and their interactions, leading to a better understanding of the schema design process as a whole. Finally, we also discuss the relationship between this simple versioning mechanism and general-purpose version-management systems.