We describe the design and performance of a number of elements based on traveling-wave electroabsorption modulators (TW-EAMs) in optical time-division-multiplexing (OTDM) and wavelength-division-multiplexing (WDM) networks. The incorporation of traveling-wave (TW) electrode design into electroabsorption modulators (EAMs) relieves the resistance-capacitance (RC) bandwidth limitation common to lumped components,. enabling higher operation speed without shortening the device. As a result, high-speed operation can be combined with essential modulator characteristics such as modulation efficiency and extinction ratio. While significant modulation bandwidth has been achieved, a lesser known aspect is that the TW electrode also provides an extra dimension for improving and enabling functionalities beyond broadband modulation. This new dimension originates from the distributed effect of the TW design and its interactions with distinctive EAM properties. This paper reviews such developments in recent years with specific applications for optical signal processing in OTDM and WDM networks. The covered functionalities include various optical gating operations for OTDM, regenerative wavelength conversions for WDM, and clock recovery.