Isotope geochemistry is in the midst of a remarkable period of innovation and discovery; the last decade (or so) has seen the emergence of ‘non traditional’ stable isotopes of metals (i.e., variations in isotopic compositions of Mg, Fe, Cu, etc.), a great expansion of mass-independent isotope geochemistry, the invention of clumped isotope geochemistry, and new capabilities for measurements of position-specific isotope effects in organic compounds. These advances stem from the emergence of multi-collector plasma mass spectrometry, innovations in gas source mass spectrometry, infrared absorption spectroscopy, and nuclear magnetic resonance techniques. These new observations demand new connections between isotope geochemistry and the chemical physics that underlies isotopic variations, including experimental study and modeling of vibrational isotope effects, photochemical isotope effects, and various nuclear volume and magnetic effects. Importantly, such collaborations also have something to offer chemists and physicists because the novel observations of emerging branches of stable isotope geochemistry hold the potential to reveal new insights into the nature of chemical bonds and reactions. This review looks broadly across the frontiers of new methods and discoveries of stable isotope geochemistry and the fundamental chemical-physics problems they pose, focusing in particular on the most pressing problems in: kinetic isotope effects in complex systems; mass independent isotope geochemistry (both the strong effects in photochemical reactions and the subtle variations of more conventional reactions); clumped isotope geochemistry; and the position-specific isotopic anatomies of organic molecules.