Gallium phosphide (GaP) is an indirect-bandgap semiconductor used widely in solid-state lighting. Despite numerous intriguing optical properties—including large χ(2) and χ(3) coefficients, a high refractive index (>3) and transparency from visible to long-infrared wavelengths (0.55–11 μm)—its application as an integrated photonics material has been little studied. Here, we introduce GaP-on-insulator as a platform for nonlinear photonics, exploiting a direct wafer-bonding approach to realize integrated waveguides with 1.2 dB cm−1 loss in the telecommunications C-band (on par with Si-on-insulator). High-quality (Q > 105), grating-coupled ring resonators are fabricated and studied. Employing a modulation transfer approach, we obtain a direct experimental estimate of the nonlinear index of GaP at telecommunication wavelengths: n2 = 1.1(3) × 10−17 m2 W−1. We also observe Kerr frequency comb generation in resonators with engineered dispersion. Parametric threshold powers as low as 3 mW are realized, followed by broadband (>100 nm) frequency combs with sub-THz spacing, frequency-doubled combs and, in a separate device, efficient Raman lasing. These results signal the emergence of GaP-on-insulator as a novel platform for integrated nonlinear photonics.