Photonic crystals are materials patterned with periodic dielectric structures. Since they were first proposed, in 1987, they have grown into a burgeoning research field with a rich spectrum of applications. Recent research in the field has been rapidly expanding to include nonlinear effects. Combining the compact formats and versatility of photonic crystal structures with the functionalities of optical nonlinearities could ultimately prove to be the key to tunable all-optical devices with huge impact across a broad range of disciplines, from telecommunications and quantum computing, to biology and sensing. Traditional approaches to nonlinear photonic crystals involve micro- (nano-) structuring the linear properties of a nonlinear medium. The research I wish to pursue through an IEF with the world-leading group on nanostructured ferroelectric optical materials would reverse this paradigm, to explore a brand new class of 2D periodic structures, i.e. Purely Nonlinear Photonic Crystals (PNPCs), based on micro- (nano-) structured nonlinearities. Key to the project will be the development of an integrated nonlinear nano-photonic platform in lithium niobate, a ferroelectric crystal in which the sign of the nonlinearity can be periodically modulated in space and exploited in integrated optical formats. The development of a such a nonlinear technology toolkit would enable a new class of ‘parametric’ photonic crystals which could manipulate all-optically the pathway, pulse shape, delay, spectrum and phase of multicolour light beams by means of purely nonlinear mechanisms (not via interference and diffraction as in ordinary photonic crystals). This could open a completely unexplored realm, holding promise for excitingly new physics and unprecedented possibilities for device engineering.