Nonlinear optical processes are important in many photonic applications ranging from optical communications and ultrashort pulse generation to frequency combs. Recent trend to miniaturize photonic components has created a growing demand also for nanoscale nonlinear components. This demand is difficult to answer by using conventional nonlinear materials motivating the search for alternatives. Nonlinear plasmonic metasurface cavities have recently emerged as a potential platform to enable nanoscale nonlinear optics. Despite steady progress, the so far achieved conversion efficiencies have not yet rivalled conventional materials. Here, we present our recent work to develop more efficient nonlinear metamaterials, focusing on plasmonic metasurfaces that support collective responses known as surface lattice resonances. These resonances are associated with very narrow spectral features, showing potential to dramatically boost nonlinear processes via resonant interactions. Here, we demonstrate a plasmonic metasurface operating at the telecommunications C band that exhibits a record-high quality factor exceeding 2000, demonstrating an order-of-magnitude improvement compared to existing metasurface cavities. Motivated by this experimental demonstration, we will also present numerical predictions suggesting that such nonlinear metasurfaces could soon answer the existing demand for miniaturized and/or flat nonlinear components.