We describe a principled approach for constructing non-vacuum initial data sets for the Cauchy problem in general relativity. The core idea has an interesting history of having been known in the '70s,
forgotten by the mathematical relativity community for decades, and now
independently rediscovered and rigorously demonstrated. We show how
it explains why certain techniques for generating initial data
worked well in the past, but also how it leads to new equations
with applealing physical properties when generating initial data containing
fluids. The talk will be targeted at a broad audience.