A critical review of previous mechanics models proposed for the evaluation of interfacial properties from single fibre tests is presented with regard to their applicability and limitations. New results which include the effects of some important factors, such as pre-existing fibre flaws, thermal residual stresses and matrix cracks, are provided for a single fibre fragmentation test. By comparing the stress distributions of single fibre fragment and multi-fibre fragment, a basic method to study the multi-fibre composite is introduced in order to relate the interfacial parameters to the mechanical properties of the bulk composite. Some challenging problems on fibre-matrix interfaces are discussed for future research work.