This tutorial review describes how fibre optic microarrays can be used to create a variety of sensing and measurement systems. This review covers the basics of optical fibres and arrays, the different microarray architectures, and describes a multitude of applications. Such arrays enable multiplexed sensing for a variety of analytes including nucleic acids, vapours, and biomolecules. Polymer-coated fibre arrays can be used for measuring microscopic chemical phenomena, such as corrosion and localized release of biochemicals from cells. In addition, these microarrays can serve as a substrate for fundamental studies of single molecules and single cells. The review covers topics of interest to chemists, biologists, materials scientists, and engineers.