Since the invention of optical fiber cable data transmission using light has become ubiquitous in the past years. Nonlinear optical effects, which are hardly noticed in our daily life, have become crucial and highly influential for the design and performance of advance high-capacity systems. Future optical systems will definitely require signal processing operations to be performed on data signals “on the fly” solely in the optical domain. Brillouin scattering is currently one of the most prominent nonlinear effects in optical fibers, as it has found many applications in various fields of photonics, such as slow light, new high coherent sources, filters, optical fiber sensing, etc. In this thesis we investigate a novel phenomenon based on Stimulated Brillouin Scattering, which is called dynamic Brillouin grating (DBG). Investigating the process of DBG generation in optical fibers we propose several new approaches to realize new tools for signal processing of the optical signal by using phonon-photon interactions. First an analytical model is proposed to describe localized DBG generation in optical fibers using three coupled equations for Stimulated Brillouin Scattering. Based on this model we can show how the grating is generated and which shape it has in time when two pump pulses are used with optical frequency difference equal to the Brillouin shift of the fiber. Moreover optical phase conjugation is also theoretically predicted for the optical wave reflected from DBG. Several applications of Dynamic Brillouin grating are identified and investigated. An optical signal delay line or buffer is proposed and experimentally demonstrated using DBG principle. Storage of an input optical pulse is achieved by changing the position of the localized DBG inside the fiber. Here DBG acts as a Bragg reflector for the optical pulse and change in DBG position defines the time-of-flight of the input and reflected pulse. Single pulse delays can be dynamically controlled with a buffer capacity ranging from several picoseconds to more than one microsecond. Such delays show that DBG based signal delay lines can easily outperform slow light based delay lines in terms of delay-bandwidth product. Optical delay of pulse trains is also achieved, but with maximum limited amount of delay governed by the acoustic wave decay constant, which in standard silica fibers is around 10-12 ns. Moreover microwave photonic signals can be also delayed using DBG demonstrating true time delay. In this configuration, the reflection bandwidth of the DBG defines the maximum operational radio frequency. Relation of the DBG bandwidth as a function of its length was measured and it was determined that DBG exhibits similar properties as weak uniform fiber Bragg grating (FBG). Another application of the DBG gratings is demonstrated by exploiting this phenomenon to realize microwave photonic filters. For the first time, two-, three- and four-tap microwave photonic filter configurations are realized based on DBG. Free spectral range and IV tcartsbA stop band central frequencies of the proposed microwave filters can be easily tuned by adjusting the properties and positions of DBGs. Dynamic gratings generated by amplitude modulated pump waves are used to realize optical differentiation, integration and time reversal of input optical signals. Performed experiments demonstrate that a DBG based signal processor performs operations on the complex amplitude of the input optical wave. The DBG based integrator offers high flexibility in terms of operational wavelength and variable integration time, which can be controlled by changing the DBG length. For the first time, new operations of true time reversal of several bit sequences are performed using dynamic Brillouin grating. To overcome the problem of the decay of the localized acoustic grating, a novel method based on phase modulation by pseudo-random bit sequence (PRBS) is proposed, which allows generation of localized and stationary DBG at random positions inside the fiber. Such a method opens up new possibilities for signal control, and for optical fiber sensing. Advantages and limitations of the PRBS technique in terms of signal-to-noise ratio are discussed. It is experimentally verified that PRBS generation of DBG is highly attractive for the operations on optical signals where time averaging is possible, such as in the fields of microwave photonics and distributed fiber sensing. On the other hand, it was experimentally verified that realization of the optical buffer for continuous digital data using the PRBS technique is difficult due to the substantial amount of instantaneous noise. A separate chapter of this thesis is devoted to the application of DBG to the field of distributed fiber sensing. A DBG based distributed temperature and stress sensor in polarization maintaining fibers has been realized, showing 1 cm spatial resolution, which is - to the best of our knowledge - first time, demonstrated using a pulsed-based Brillouin sensor. The demonstration is performed in a 20 m fiber, but the sensing range of the proposed DBG based sensor can be expanded up to several hundred meters. In addition, it is shown that the demonstrated spatial resolution is not the ultimate limit, and a finer spatial resolution can be achieved by simply reducing the probe pulse duration. Another Brillouin distributed temperature and stress sensor is proposed based on the DBG principle. Here DBG is generated by modulating the phases of a continuous Brillouin pump and probe waves by common PRBS with unipolar encoding and modulation speeds faster than phonon lifetime. By choosing the proper parameters of PRBS, only one localized and permanent dynamic Brillouin grating is placed inside the sensing fiber. Distributed measurements of temperature or strain are accomplished by scanning the position of the DBG inside the fiber and determining the Brillouin resonance condition at each position. Using this technique, a random access sensor with 1 cm spatial resolution is demonstrated over a 40 m standard single mode fiber. In the proposed scheme the spatial resolution can be easily changed by changing the bit duration of the PRBS, while the measurement range is controlled by the length of the PRBS sequence.