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This thesis presents results of a research on applications of Brillouin dynamic gratings - distributed reflectors that can be dynamically created in an optical fibre by two optical waves. A basic theory of stimulated Brillouin scattering (SBS) is introduced, on a level enough for understanding the processes that govern SBS. A major part of this thesis is dedicated to studies of distributed Brillouin sensors based on phase correlation. First, the concept of correlation-based sensors is introduced - the commonly used Brillouin optical correlation-domain analysis (BOCDA) and the phase-correlation technique. It is described how the Brillouin interaction between two waves can be localised, creating a permanent reflector confined to a centimetre-scale section of the fibre. This allows creating a distributed sensing system with very a high spatial resolution. A detailed theoretical model for the phase-correlation technique is presented, showing how the gain response of a system can be calculated and how the system resolution can be determined. For an ideal case an analytical solution is derived, while for real experimental conditions the expected behaviour is found via numerical simulation. Results of numerical modelling are compared with experimentally obtained data, showing a good agreement. A spatial resolution of 1 cm is demonstrated over a 200 m distance representing 20000 separate points. The concept of time gating is introduced, extending the measurement distance from 200 m to 17.5 km while retaining a sub-centimetre spatial resolution. This technique allows for a two order of magnitude increase in the number of points that a system is capable to resolve. An absolute record for distributed fibre sensors is achieved, demonstrating a system capable to resolve 2100000 separate points. Limitations for a further increase in number of points are discussed as well as possible ways to overcome them. An issue related to the temperature dependency of the refractive index is discussed in details, since it can lead to significant errors in spatial accuracy. An algorithm is presented that is capable of using the measured temperature change to account for the change in the refractive index and correctly determine the positioning of measured data. In the last chapter potential applications of Bragg dynamic gratings in signal processing are investigated. A theoretical model of BDG's in polarisation-maintaining fibres is presented capable of calculating reflection of a probe wave - continuous or pulsed. The model includes the case of non-uniform birefringence along the fibre. Dynamic gratings are applied to create a flip-flop - an all-optical memory, turned on and off by a light pulse. A working system is demonstrated in a 1 m long fibre, corresponding to a 10 ns storage time. Using the theoretical model the birefringence variation is measured along the fibre. A preliminary study of spectral properties of dynamic gratings is presented, along with a model predicting the spectrum of a uniform BDG. It is demonstrated that the spectral properties of a BDG can be manipulated by changing the spectra of optical waves used in the generation process. This work is concluded by a discussion, summing up the above-mentioned theoretical the experimental work. Potential applications of the presented research are proposed along with the most promising direction of further research activities.