  Universal spacetimes are exact solutions to all higher-order theories of
gravity. We study these spacetimes in four dimensions and provide necessary and
sufficient conditions for universality for all Petrov types except of type II.
We show that all universal spacetimes in four dimensions are algebraically
special and Kundt. Petrov type D universal spacetimes are necessarily direct
products of two 2-spaces of constant and equal curvature. Furthermore, type II
universal spacetimes necessarily possess a null recurrent direction and they
admit the above type D direct product metrics as a limit. Such spacetimes
represent gravitational waves propagating on these backgrounds. Type III
universal spacetimes are also investigated. We determine necessary and
sufficient conditions for universality and present an explicit example of a
type III universal Kundt non-recurrent metric.
