All pathways which limit global temperature rise to <2°C above pre-industrial temperatures now require carbon dioxide removal (CDR) in addition to rapid greenhouse gas emissions reductions. Novel and durable CDR strategies need to rapidly scale over the next few decades in order to reach Paris Agreement Targets. Terrestrial enhanced weathering (EW) involves the acceleration of natural weathering processes via the deployment of crushed rock feedstocks, typically Ca- and Mg-rich silicates, in soils. While models predict this has the potential to remove multiple gigatonnes of CO2 annually, as an open-system pathway, the measurement (monitoring), reporting, and verification (MRV) of carbon removal and storage is challenging. Here we provide a review of the current literature showing the state-of-play of different methods for monitoring EW. We focus on geochemical characterization of weathering processes at the weathering site itself, acknowledging that the final storage of carbon is largely in the oceans, with potential losses occurring during transfer. There are two main approaches for measuring EW, one focused on solid phase measurements, including exchangeable phases, and the other on the aqueous phase. Additionally, gas phase measurements have been employed to understand CO2 fluxes, but can be dominated by short-term organic carbon cycling. The approaches we review are grounded in established literature from the natural environment, but implementing these approaches for EW CDR quantification has strengths and limitations. The complexity inherent in open-system CDR pathways is navigable through surplus measurement strategies and well-designed experiments, which we highlight are critical in the early stage of the EW CDR industry.