37 pagesInternational audienceThe main modelling methods devoted to microstrutured air-silica optical fibres (MOFs) are presented and discussed. Then, the specific propagation properties of MOFs are studied in detail. Characteristics measured on fibres manufactured in our laboratory or reported in the literature are analysed. A large number of potential and demonstrated applications are presented and the obtained performances are discussed. A particular attention is given to hollow- core photonic bandgap fibres and their applications