Gallium phosphide (GaP) is an indirect bandgap semiconductor used widely in solid-state lighting. Despite numerous intriguing optical properties---including large $chi^{(2)}$ and $chi^{(3)}$ coefficients, a high refractive index ($>3$), and transparency from visible to long-infrared wavelengths ($0.55-11,mu$m)---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 loss in the telecommunications C-band (on par with Si-on-insulator). High quality $(Q> 10^5)$, 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: $n_2=1.2(5)times 10^{-17},text{m}^2/text{W}$. 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.