Calcium carbonate (CaCO3) and its structural relatives, the phosphates and hydroxyapatites, are natural crystals which are similar to the minerals found in such hard tissues as teeth and bone. We have recently demonstrated that laser- induced material removal in calcium carbonate occurs with high efficiency when irradiating with a free-electron laser at the fundamental asymmetric stretch mode of the carbonate group near 7 micrometers ; related studies show that the same thing is true in the isoelectronic sodium nitrate, and we expect it to operate in the phosphates as well when irradiated near the resonant 9 micrometers band. The mechanism of material removal appears to be the ejection of CO followed by a calcination reaction which produces CaO. Among the features which make CaCO3 such an interesting model material is that it also has a characteristic, temperature-dependent thermoluminescence - thus making it possible, by the study of the light emitted by the crystal prior to and after ablation, to estimate the temperature reached by the crystal in the early stages of laser ablation. Wavelength-dependent photoluminescence, photoacoustic and plume-spectroscopic studies show that efficient evaporative 'hole drilling' occurs at the infrared wavelengths corresponding to carbonate or nitrate vibration modes. However, where electronic or vibrational defects are excited by visible or infrared lasers, respectively, the mechanisms of material removal are photomechanical fracture in the former case and exfoliation or subsurface explosive vaporization in the latter.