Hollow-core photonic-crystal fibres (PCFs) for the delivery of high-fluence laser radiation capable of ablating tooth enamel are developed. Sequences of picosecond pulses of 1.06 microm Nd:YAG-laser radiation with a total energy of about 2 mJ are transmitted through a hollow-core photonic-crystal fibre with a core diameter of approximately 14 microm and are focused on a tooth surface in vitro to ablate dental tissue. The hollow-core PCF is shown to support the single-fundamental-mode regime for 1.06 microm laser radiation, serving as a spatial filter and allowing the laser beam quality to be substantially improved. The same fibre is used to transmit emission from plasmas produced by laser pulses on the tooth surface in the backward direction for detection and optical diagnostics.