Ultrafast optical excitation, especially when resonant to specific lattice modes, has recently emerged as a powerful means to control complex solids and their phase transitions. One of the most ambitious applications of these optical methods is the possibility to manipulate the lattice and the electronic interactions to bring about nonequilibrium superconductivity at temperatures far above the thermodynamic critical temperature Tc. In this talk, I will discuss how midinfrared optical excitation of the BCS-like superconductor K3C60 led to an emergent nonequilibrium superconducting-like phase above its equilibrium Tc. This light-induced state is suppressed by external pressure, as expected for a conventional BCS superconductor, but its microscopic origin is still unclear. In order to further our understanding of these phenomena, it is necessary to go beyond ultrafast optics and instead probe electronic excitations at finite momentum. I will report the recent observation of collective, finite-momentum dynamics of a charge order condensate in the cuprate La2-xBaxCuO4 using next-generation time-resolved X-ray scattering methods. Finally, I will discuss how ultrafast electron and X-ray scattering will enable the observation of novel nonlinear effects in the charge, spin and lattice response of complex solids.