60 years of nonlinear optics have been marked a number of significant achievements, but for the most part, all of these breakthroughs occurred in the first 10-15 years, after which the progress has been lamentably slow. In my view, the reason for this slowdown has been the fact that the fundamental limits of nonlinear optics in terms of strength and speed of the effects have already been reached, and the powers required for many nonlinear schemes are plainly too high for them to be practical. In this talk I explain the very fundamental origins of the strength-speed trade-off in nonlinear optics, distinguishing between the instant and slow nonlinearities. Then I explore the resonant enhancement of nonlinearities using intrinsic or extrinsic resonances. Using this framework, I will explore the recently widely promoted nonlinearities in graphene, other 2D materials and epsilon near zero materials, as well as newly minted enhancement schemes like Fano resonances, exceptional points, bound states in continuum and so on. Sober but hopefully not entirely useless, conclusions will be drawn.
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