Optical signal generation and processing are becoming increasingly important for a wide range of scientific and engineering applications, including high-speed optical telecommunications, optical computing circuits, optical biomedical imaging, advanced sensors and material/device characterization techniques. Optical approaches offer the possibility to overcome the severe speed limitations of present electronic circuits, which are practically limited to generation/processing speeds below a few tens of GHz. All-optical circuits would easily enable generation/processing speeds covering frequency bandwidths from 10s of GHz to several THz. As for conventional waveform generation/processing circuits in electronics, fundamental devices in the optical domain, such as basic processing functions and customized waveform generation schemes need to be realized and developed. Among all-optical implementation approaches, all-fiber technologies, e.g. fiber long period grating (LPG) and Bragg grating (BG), are attractive due to their simplicity, potential for low cost and full compatibility with fiber-optics and integrated-waveguide systems. The spatial resolution limitation of presently available fiber grating fabrication technologies has limited the fiber-based waveform generation/processing schemes to temporal resolutions of at least several picoseconds, i.e. corresponding to a few 100s of GHz in terms of the bandwidth of waveform generation/processing. In this work, we present our recent research results demonstrating that arbitrary optical waveforms with bandwidths well in the THz regime can be generated/processed using fiber LPG device. The proposed LPG solutions enable one to synthesize/process optical waveforms with temporal resolutions down to the femtosecond range, i.e. far faster operation bandwidths than conventional BG-based optical waveform generation/processing schemes.