Brillouin scattering is an interaction between light and sound in a material. This inelastic light scattering had been observed in the first optical fibres that were used in cross-continent communication. Via Brillouin scattering, the guided light wave in an optical fibre is back-scattered by the thermally generated high frequency acoustic waves and undergo Doppler frequency shift. Owing to the sensitivity of acoustic velocity to the change of temperature and strain, Brillouin scattering has been widely used in distributed fibre sensors and its resolution, distance range and speed of measurements have been tremendously improved. However, all reported distributed Brillouin fibre sensors incorporate the axial propagating acoustic wave and thus limited to detecting physical parameters inside the fibre core. In this thesis, distinct classes of Brillouin scatterings in optical fibres are explored and analysed in distributed fashion. Apart from the axial propagating acoustic wave, optical fibre supports a huge variety of elastic vibrations. In the first part, surface and hybrid Brillouin scatterings are studied by using the tapered optical fibre. As the diameter of optical fibre approaches subwavelength range (diameter ~1um), the material properties contrast at the boundary of microfibre (the central part of the tapered optical fibre) gives rise to Rayleigh wave which propagates on the surface. This type of Brillouin scattering as well as the other acoustic resonances along the transition region of the tapered fibre are measured using a distributed Brillouin analysis technique based on phase correlation. In the second part, forward stimulated Brillouin scattering (FSBS) in standard single-mode fibres (SMF) is explored as a new type of sensor that allows materials surrounding the optical fibre to affect the phase of the guided light. FSBS is an interaction between the guided light and the transverse acoustic waves which are stimulated through electrostriction and resonate within the fibre cross-section due to the acoustic reflection at its boundary. The variation of the acoustic impedance mismatch between the fibre bulk and the external material affects the boundary reflectivity and modify the acoustic decay rate. An experiment has been performed to demonstrate the feasibility to measure acoustic impedance of several liquids through FSBS. As the scattered light of FSBS is in forward direction, obtaining its distributed profile along a fibre is a challenge due to the absence of time-of-flight information. In order to overcome this problem, the local response of FSBS is recovered through measuring the sidebands progression of a light pulse using the backward Brillouin scattering.