Microstructured optical fibres (MOFs) have attracted much interest in recent times, due to their unique waveguiding properties that are vastly different from those of conventional step-index fibres. Tapering of these MOFs promises to significantly extend and enhance their capabilities. In this paper, we review the fabrication and characterisation techniques of these fibr e tapers, and explore their fundamental waveguiding properties and potential applications. We fabricate photonic crystal fibre tapers without collapsing the air-holes, and confirm this with a non-invasive probing technique that enables the characterisation of the internal microstructure along the taper. We then describe the fundamental property of such tapers associated with the leakage of the core mode that leads to long-wavelength loss, influencing the operational bandwidth of these tapers. We also revisit the waveguiding properties in another form of tapered MOF photonic wires, which transition through waveguiding regimes associated with how strongly the mode is isolated from the external environment. We explore these regimes as a potential basis for evanescent field sensing applications, in which we can take advantage of air-hole collapse as an extra dimension to these photonic wires.