This paper gives a review of a proposed fully-distributed fiber-optic sensing technique based on a traveling long-period grating (LPG) in a single-mode optical fiber. The LPG is generated by pulsed acoustic waves that propagate along the fiber. Based on this platform, first we demonstrated the fully-distributed temperature measurement in a 2.5m fiber. Then by coating the fiber with functional coatings, we demonstrated fully-distributed biological and chemical sensing. In the biological sensing experiment, immunoglobulin G (IgG) was immobilized onto the fiber surface, and we showed that only specific antigen-antibody binding can introduce a measurable shift in the transmission optical spectrum of the traveling LPG when it passes through the pretreated fiber segment. In the hydrogen sensing experiment, the fiber was coated with a platinum (Pt) catalyst layer, which is heated by the thermal energy released from Pt-assisted combustion of H2 and O2, and the resulted temperature change gives rise to a measurable LPG wavelength shift when the traveling LPG passes through. Hydrogen concentration from 1% to 3.8% was detected in the experiment. This technique may also permit measurement of other quantities by changing the functional coating on the fiber; therefore it is expected to be capable of other fully-distributed sensing applications.