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Nonlinear photonic chips can generate and process signals all-optically with far superior performance to that possible electronically — particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics, its high two-photon absorption at telecommunication wavelengths poses a fundamental limitation. We review recent progress in non-silicon CMOS-compatible platforms for nonlinear optics, with a focus on Si₃N₄ and Hydex^®. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement. We highlight their potential future impact as well as the challenges to achieving practical solutions for many key applications.