Photonic crystal fibres have been shown to provide new waveguiding properties compared to standard optical fibres. Among the novel aspects of these fibres are wider single-mode range, new bending loss limitations, excessive spotsize control, and extended dispersion modification (e.g., dispersion zero in the visible range and near-zero dispersion-flattened operation), and air-guiding core structures. In this presentation, we present recent theoretical results on the waveguiding properties of high-index-core and low-index-core photonic crystal fibres, and compare these results with alternative methods and experimental results.