With high-bandwidth and on-demand applications continuing to emerge, next-generation core optical networks will likely require significant improvements in reconfigurability and ultra-fast operations. Optical signal processing overcomes the electronic bandwidth limitations with the advantages in terms of transparency and scalability. We review recent progresses in all-optical signal processing potentially for ultrahigh speed systems and networks. Starting from a brief overview of optical signal processing in high-speed optical systems and networks, we highlight a few key network functionalities, including optical logic operations, reconfigurable add/drop multiplexing, optical regeneration, wavelength conversion, format conversion, and phase-sensitive amplification. Different techniques are investigated and discussed, employing a wide range of devices and various nonlinearities. Some of experimental results are presented in both single polarization systems and polarization-division multiplexing systems.