This book provides two state-of-the-art quantitative techniques to determine ultra-trace rare earth elements (REEs) in natural carbonates using solution nebulization-inductively coupled plasma mass spectrometry (SN-ICPMS) and laser ablation-inductively coupled plasma mass spectrometry (LA-ICPMS) with respective applications were presented in this dissertation. These techniques were applied to natural carbonates, including corals and stalagmites, to understand volcano eruptions and the impacts on modern biosystem and paleoclimate regimes.