In this communication, we report on the design, fabrication, and testing of Silicon Nitride on Insulator (SiNOI) and Aluminum-Gallium-Arsenide (AlGaAs) on silicon-on-insulator (SOI) nonlinear photonic circuits for continuum generation in Silicon (Si) photonics. As recently demonstrated, the generation of frequency continua and supercontinua can be used to overcome the intrinsic limitations of nowadays silicon photonics notably concerning the heterogeneous integration of III-V on SOI lasers for datacom and telecom applications. By using the Kerr nonlinearity of monolithic silicon nitride and heterointegrated GaAs-based alloys on SOI, the generation of tens or even hundreds of new optical frequencies can be obtained in dispersion tailored waveguides, thus providing an all-optical alternative to the heterointegration of hundreds of standalone III-V on Si lasers. In our work, we present paths to energy-efficient continua generation on silicon photonics circuits. Notably, we demonstrate spectral broadening covering the full C-band via Kerrbased self-phase modulation in SiNOI nanowires featuring full process compatibility with Si photonic devices. Moreover, AlGaAs waveguides are heterointegrated on SOI in order to dramatically reduce (x1/10) thresholds in optical parametric oscillation and in the power required for supercontinuum generation under pulsed pumping. The manufacturing techniques allowing the monolithic co-integration of nonlinear functionalities on existing CMOS-compatible Si photonics for both active and passive components will be shown. Experimental evidence based on self-phase modulation show SiNOI and AlGaAs nanowires capable of generating wide-spanning frequency continua in the C-Band. This will pave the way for low-threshold power-efficient Kerr-based comb- and continuum- sources featuring compatibility with Si photonic integrated circuits (Si-PICs).