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This tutorial highlights challenges and opportunities in achieving efficient flexible optical networks. Optical signal processing may potentially increase network flexibility because of its functions' transparency, tunability, and reconfigurability. We review recent advances in high-speed optical signal processing techniques that might enable flexible networks. Various optical approaches that enable key functions are discussed, including format conversion, increases in spectral efficiency, and phase-sensitive operations. We also discuss the potential utilization of basic enabling technologies, such as optical frequency combs and optical nonlinear devices.