Fibre optic technology lends yet another dimensions to the topic of optical signal processing complementing both Fourier plane and digital optical approaches. It is inevitable that eventually optical signal processing will combine all three of these basic concepts. However, in this paper we consider the possibilities offered by the fibre optic transmission medium in the context of signal processing. The unique features of the transmission medium imply that precise frequency domain filters may be readily realised. Furthermore, functions such as matrix-matrix multiplication and code recognition may also be programmed in the all optical fibre form. These processes are essentially linear but the addition of a simple non-linear element may yet further extend the capability of these basic concepts. This paper outlines the general principles underlying fibre optic signal processing and gives some indication of its performance potential.