Abstract: The KPZ equation was introduced in the eighties as a model of surface growth, but it was soon realised that its solution is a much more "universal" object describing the crossover between the Gaussian universality class and the KPZ universality class. The mathematical proof of its universality however is still an open problem, in particular because of the lack of a good approximation theory for the equation. In this talk, we present a new, robust, notion of solution to the KPZ equation. Our approach allows to factor the solution map into a "universal" (i.e. independent of initial condition) measurable map, composed with an "abstract" solution map with very good continuity properties. This lays the foundations for a robust approximation theory to the KPZ equation, which is needed to prove its universality. As a byproduct of the construction, we obtain very detailed regularity estimates on the solutions, as well as a new homogenisation result.